Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 May 2010
Posts: 1

John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
24 May 2010, 14:15
Question Stats:
44% (02:52) correct 56% (03:09) wrong based on 266 sessions
HideShow timer Statistics
John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits? A. 15/16 B. 11/16 C. 11/12 D. 1/2 E. 5/8
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 65062

Re: Phone number
[#permalink]
Show Tags
25 May 2010, 03:46
scaredshikless wrote: 25. John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
A. 15/16 B. 11/16 C. 11/12 D. 1/2 E. 5/8
I don't understand the explanation to this one (so I obviously got it wrong...).
Also, at first, I read it as 1 only appears once in the last three places. If that were the case, how would you solve this?
Thanks, folks. The phone numbers is of a type: {X}{X}{X}{X}{1}{1}{1}. {X}'s can take following values: 4 primes {2, 3, 5, 7} and 4 nonprimes {4, 6, 8, 9}. Total 8 choices for each {X}. Probability that {X} will be prime is therefore \(\frac{4}{8}=\frac{1}{2}\) and probability of {X} will not be a prime is again \(\frac{1}{2}\). We want at least 2 {X}'s out of 4 to be primes, which means 2, 3 or 4 primes. Let's count the opposite probability and subtract it from 1. Opposite probability of at least 2 primes is 0 or 1 prime: So {P}{NP}{NP}{NP} and {NP}{NP}{NP}{NP}. Scenario 1 prime  {P}{NP}{NP}{NP}: \(\frac{4!}{3!}*\frac{1}{2}*(\frac{1}{2})^3=\frac{4}{16}\). We are multiplying by \(\frac{4!}{3!}\) as scenario {P}{NP}{NP}{NP} can occur in several different ways: {P}{NP}{NP}{NP}, {NP}{P}{NP}{NP}, {NP}{NP}{P}{NP}, {NP}{NP}{NP}{P}  4 ways (basically the # of permutations of 4 objects out ow which 3 are the same). Scenario 0 prime  {NP}{NP}{NP}{NP}: \((\frac{1}{2})^4=\frac{1}{16}\). Hence opposite probability = \(\frac{4}{16}+\frac{1}{16}=\frac{5}{16}\). So probability of at least 2 primes is: 1(Opposite probability) = \(1\frac{5}{16}=\frac{11}{16}\) Answer: B.
_________________




VP
Joined: 27 May 2012
Posts: 1070

Re: Phone number
[#permalink]
Show Tags
10 Sep 2012, 13:35
Bunuel wrote: scaredshikless wrote: 25. John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
A. 15/16 B. 11/16 C. 11/12 D. 1/2 E. 5/8
I don't understand the explanation to this one (so I obviously got it wrong...).
Also, at first, I read it as 1 only appears once in the last three places. If that were the case, how would you solve this?
Thanks, folks. The phone numbers is of a type: {X}{X}{X}{X}{1}{1}{1}. {X}'s can take following values: 4 primes {2, 3, 5, 7} and 4 nonprimes {4, 6, 8, 9}. Total 8 choices for each {X}. Probability that {X} will be prime is therefore \(\frac{4}{8}=\frac{1}{2}\) and probability of {X} will not be a prime is again \(\frac{1}{2}\). We want at least 2 {X}'s out of 4 to be primes, which means 2, 3 or 4 primes. Let's count the opposite probability and subtract it from 1. Opposite probability of at least 2 primes is 0 or 1 prime: So {P}{NP}{NP}{NP} and {NP}{NP}{NP}{NP}. Scenario 1 prime  {P}{NP}{NP}{NP}: \(\frac{4!}{3!}*\frac{1}{2}*(\frac{1}{2})^3=\frac{4}{16}\). We are multiplying by \(\frac{4!}{3!}\) as scenario {P}{NP}{NP}{NP} can occur in several different ways: {P}{NP}{NP}{NP}, {NP}{P}{NP}{NP}, {NP}{NP}{P}{NP}, {NP}{NP}{NP}{P}  4 ways (basically the # of permutations of 4 objects out ow which 3 are the same). Scenario 0 prime  {NP}{NP}{NP}{NP}: \((\frac{1}{2})^4=\frac{1}{16}\). Hence opposite probability = \(\frac{4}{16}+\frac{1}{16}=\frac{5}{16}\). So probability of at least 2 primes is: 1(Opposite probability) = \(1\frac{5}{16}=\frac{11}{16}\) Answer: A. Just a small confusion 2,3,5,7 are primes , and 1,4,6,8,9 non primes ,just because there are 3 one's in the last three places it doesn't mean that 1 cannot be at any other place, question says boy remembers last three places having one's and not that there are only 3 ones in the 7 digit number the phone number could be {1 2 3 6 1 1 1 } this has two primes and 5 non primes and 4 one's or { 8 2 2 6 1 1 1 } this has 2 primes and all the primes are same first going the long way p( 2 primes ) +p( 3 primes )+p(4 primes ) \(\frac{4}{9} * \frac{4}{9} * \frac{5}{9} *\frac{5}{9} *1*1*1* \frac{4!}{2!2!}\) ( exactly two primes ) Multiplying by \(\frac{4!}{2!2!}\) as we can permutate only the first 4 digits , the last are fixed (1,1,1) \(\frac{4}{9} * \frac{4}{9}* \frac{4}{9}*\frac{5}{9}*1*1*1 *\frac{4!}{3!}\) ( exactly 3 primes )( 3 of a kind ) \(\frac{4}{9} *\frac{4}{9} *\frac{4}{9} *\frac{4}{9} * 1,1,1\) ( exactly 4 primes ) Now for the case 2 primes, both the primes could be same or different then how does the notation \(\frac{4!}{2!2!}\) change , or does it remain the same ? Similarly for the case of 3 primes the primes could be 2,2,2 all same or 2,3,5 all different then how does the notation \(\frac{4!}{3! }\) change or does it remain the same? In this question we are taking primes as one kind and non primes as other kind , so it doesn't matter if the primes are all same or all different ? Is this statement correct? 1) Please could you show how to do this sum individual probability way as I have tried above ? 2) Also please consider the fact that 1 may have to be included as a non prime as the question does not explicitly state that there are only 3 ones in the phone number , he only remembers that the last three are ones.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India

Re: Phone number
[#permalink]
Show Tags
11 Sep 2012, 22:05
stne wrote: Just a small confusion 2,3,5,7 are primes , and 1,4,6,8,9 non primes ,just because there are 3 one's in the last three places it doesn't mean that 1 cannot be at any other place, question says boy remembers last three places having one's and not that there are only 3 ones in the 7 digit number the phone number could be {1 2 3 6 1 1 1 } this has two primes and 5 non primes and 4 one's or { 8 2 2 6 1 1 1 } this has 2 primes and all the primes are same
first going the long way p( 2 primes ) +p( 3 primes )+p(4 primes )
\(\frac{4}{9} * \frac{4}{9} * \frac{5}{9} *\frac{5}{9} *1*1*1* \frac{4!}{2!2!}\) ( exactly two primes ) Multiplying by \(\frac{4!}{2!2!}\) as we can permutate only the first 4 digits , the last are fixed (1,1,1)
\(\frac{4}{9} * \frac{4}{9}* \frac{4}{9}*\frac{5}{9}*1*1*1 *\frac{4!}{3!}\) ( exactly 3 primes )( 3 of a kind )
\(\frac{4}{9} *\frac{4}{9} *\frac{4}{9} *\frac{4}{9} * 1,1,1\) ( exactly 4 primes )
Now for the case 2 primes, both the primes could be same or different then how does the notation \(\frac{4!}{2!2!}\) change , or does it remain the same ?
Similarly for the case of 3 primes the primes could be 2,2,2 all same or 2,3,5 all different then how does the notation \(\frac{4!}{3! }\) change or does it remain the same?
In this question we are taking primes as one kind and non primes as other kind , so it doesn't matter if the primes are all same or all different ? Is this statement correct?
1)Please could you show how to do this sum individual probability way as I have tried above ?
2)Also please consider the fact that 1 may have to be included as a non prime as the question does not explicitly state that there are only 3 ones in the phone number , he only remembers that the last three are ones.
Yes, it does seem that the language of the question is not clear. When I read the question, I also assumed 4 prime digits and 5 non prime (including 1). After all, the question only says that 1 appears in the last 3 places (and hence, we can ignore the last 3 places). It doesn't say that 1 does not appear anywhere else. But it seems that it might also imply that 1 appears only in the last 3 places (looking at the options, that was their intention). Anyway, I am sure that if this question actually appears and they mean to say that 1 cannot be at any other place, they will definitely mention it. Let's calculate the probability of different number of prime numbers: 0 primes Probability = (5/9)*(5/9)*(5/9)*(5/9) 1 prime Probability = (4/9)*(5/9)*(5/9)*(5/9)*4 (there are 4 positions for the prime) 2 primes Probability = (4/9)*(4/9)*(5/9)*(5/9)*4C2 (select 2 of the 4 positions for the primes) 3 primes Probability = (4/9)*(4/9)*(4/9)*(5/9)*4 (4 positions for the non prime) 4 primes Probability = (4/9)*(4/9)*(4/9)*(4/9) Probability of at least 2 primes = 1  (Probability of 0 prime + Probability of 1 prime) Probability of at least 2 primes = Probability of 2 primes + Probability of 3 primes + Probability of 4 primes The calculations are painful so let's leave it here. As I said, their intention was probability of prime = 1/2, probability of composite = 1/2 which makes the calculations simple. The 4 positions are different but you can have the same prime on one or more positions. When you say 4/9, you are including all cases (2, 3, 5, 7) so you don't need to account for them separately. When you say, (4/9)*(4/9)*(4/9)*(4/9), you are including all cases e.g. (2222, 2353, 3577, 2357 etc). All you need to do it separate out the primes and the non primes. That you do by arranging primes and non primes as NNPP or NPNP or PPNN etc (as we did above)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



VP
Joined: 27 May 2012
Posts: 1070

Re: Phone number
[#permalink]
Show Tags
12 Sep 2012, 08:27
VeritasPrepKarishma wrote: stne wrote: Just a small confusion 2,3,5,7 are primes , and 1,4,6,8,9 non primes ,just because there are 3 one's in the last three places it doesn't mean that 1 cannot be at any other place, question says boy remembers last three places having one's and not that there are only 3 ones in the 7 digit number the phone number could be {1 2 3 6 1 1 1 } this has two primes and 5 non primes and 4 one's or { 8 2 2 6 1 1 1 } this has 2 primes and all the primes are same
first going the long way p( 2 primes ) +p( 3 primes )+p(4 primes )
\(\frac{4}{9} * \frac{4}{9} * \frac{5}{9} *\frac{5}{9} *1*1*1* \frac{4!}{2!2!}\) ( exactly two primes ) Multiplying by \(\frac{4!}{2!2!}\) as we can permutate only the first 4 digits , the last are fixed (1,1,1)
\(\frac{4}{9} * \frac{4}{9}* \frac{4}{9}*\frac{5}{9}*1*1*1 *\frac{4!}{3!}\) ( exactly 3 primes )( 3 of a kind )
\(\frac{4}{9} *\frac{4}{9} *\frac{4}{9} *\frac{4}{9} * 1,1,1\) ( exactly 4 primes )
Now for the case 2 primes, both the primes could be same or different then how does the notation \(\frac{4!}{2!2!}\) change , or does it remain the same ?
Similarly for the case of 3 primes the primes could be 2,2,2 all same or 2,3,5 all different then how does the notation \(\frac{4!}{3! }\) change or does it remain the same?
In this question we are taking primes as one kind and non primes as other kind , so it doesn't matter if the primes are all same or all different ? Is this statement correct?
1)Please could you show how to do this sum individual probability way as I have tried above ?
2)Also please consider the fact that 1 may have to be included as a non prime as the question does not explicitly state that there are only 3 ones in the phone number , he only remembers that the last three are ones.
Yes, it does seem that the language of the question is not clear. When I read the question, I also assumed 4 prime digits and 5 non prime (including 1). After all, the question only says that 1 appears in the last 3 places (and hence, we can ignore the last 3 places). It doesn't say that 1 does not appear anywhere else. But it seems that it might also imply that 1 appears only in the last 3 places (looking at the options, that was their intention). Anyway, I am sure that if this question actually appears and they mean to say that 1 cannot be at any other place, they will definitely mention it. Let's calculate the probability of different number of prime numbers: 0 primes Probability = (5/9)*(5/9)*(5/9)*(5/9) 1 prime Probability = (4/9)*(5/9)*(5/9)*(5/9)*4 (there are 4 positions for the prime) 2 primes Probability = (4/9)*(4/9)*(5/9)*(5/9)*4C2 (select 2 of the 4 positions for the primes) 3 primes Probability = (4/9)*(4/9)*(4/9)*(5/9)*4 (4 positions for the non prime) 4 primes Probability = (4/9)*(4/9)*(4/9)*(4/9) Probability of at least 2 primes = 1  (Probability of 0 prime + Probability of 1 prime) Probability of at least 2 primes = Probability of 2 primes + Probability of 3 primes + Probability of 4 primes The calculations are painful so let's leave it here. As I said, their intention was probability of prime = 1/2, probability of composite = 1/2 which makes the calculations simple. The 4 positions are different but you can have the same prime on one or more positions. When you say 4/9, you are including all cases (2, 3, 5, 7) so you don't need to account for them separately. When you say, (4/9)*(4/9)*(4/9)*(4/9), you are including all cases e.g. (2222, 2353, 3577, 2357 etc). All you need to do it separate out the primes and the non primes. That you do by arranging primes and non primes as NNPP or NPNP or PPNN etc (as we did above) Thank you karishma, since there was no response for a while I thought my query was unreasonable, good to see at least some people appreciated what I wrote . Highly appreciate your response. Great so now I know probability of one prime 4/9* 5/9 * 5/9 *5/9 * 4= 2000/6561 PROBABILITY of 0 prime's = 5/9*5/9*5/9*5/9= 625/6561 probability of at least 2 primes = 1 ( 2000/6561 + 625/6561) 1(2625/6561) = 3936/6561 = .59 now lets check by doing long way 2 primes 4/9 * 4/9 * 5/9*5/9* 4!/2!2! = 2400/6561 ( PPNN : two primes could be same ,2 , 2 or different 2, 3 doesn't matter we can think of this as, two of a kind and two of another kind ,hence 4!/2!2!) 3 primes 4/9 *4/9 *4/9*5/9*4 = 1280/6561 (4!/3! = 4) Three of one kind again PPPN. 4 primes 4/9*4/9*4/9*4/9 = 256/6561 all of the same kind , hence only one way to select them. PPPP total 3936/6561 = .59 Bingo! hence we can see both ways we are getting the same result. Karishma if there is any error in my understanding, please do point out, I have considered primes as one kind and non primes as another kind instead of the position logic which you have mentioned.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India

Re: Phone number
[#permalink]
Show Tags
12 Sep 2012, 19:42
stne wrote: Great so now I know probability of one prime 4/9* 5/9 * 5/9 *5/9 * 4= 2000/6561
PROBABILITY of 0 prime's = 5/9*5/9*5/9*5/9= 625/6561
probability of at least 2 primes = 1 ( 2000/6561 + 625/6561) 1(2625/6561) = 3936/6561 = .59
now lets check by doing long way
2 primes
4/9 * 4/9 * 5/9*5/9* 4!/2!2! = 2400/6561 ( PPNN : two primes could be same ,2 , 2 or different 2, 3 doesn't matter we can think of this as, two of a kind and two of another kind ,hence 4!/2!2!)
3 primes
4/9 *4/9 *4/9*5/9*4 = 1280/6561 (4!/3! = 4) Three of one kind again PPPN.
4 primes
4/9*4/9*4/9*4/9 = 256/6561 all of the same kind , hence only one way to select them. PPPP
total 3936/6561 = .59 Bingo!
hence we can see both ways we are getting the same result.
Karishma if there is any error in my understanding, please do point out, I have considered primes as one kind and non primes as another kind instead of the position logic which you have mentioned.
Everything seems to be in order. It doesn't matter whether you choose to think in terms of position or arrangement of Ps and Ns. The result would be the same. When I need all arrangements of PNNN, I can write it as 4!/3! (= 4) or I can say that I will select one place for the P in 4 different ways. Either ways, we are arranging a P and 3 Ns.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



VP
Joined: 06 Sep 2013
Posts: 1491
Concentration: Finance

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
08 May 2014, 08:24
Nice problem but I think we should change the language just to clarify that 1 can't be used again even if it appears on te last 4 digits. Thanks mods Cheers! J



Manager
Joined: 24 Mar 2010
Posts: 71

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
31 Jul 2014, 06:14
jlgdr wrote: Nice problem but I think we should change the language just to clarify that 1 can't be used again even if it appears on te last 4 digits. Thanks mods Cheers! J I agree that we should change the language so that the question will be clearer than now. At first I also assume that 1 appears once within 3 last places.
_________________
Start to fall in love with GMAT <3



Intern
Joined: 25 Dec 2012
Posts: 16

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
14 Aug 2014, 13:22
Hi! I have a question here. What does is wrong if we do this in this way? Outcome wanted/Total outcome. This means:
Outcome wanted: 4*4*8*8*1*1*1. I have in the first and in the second digit, 4 possibles numbers (just primes). For the third and fourth digit are 8 possible numbers (2,3,4,5,6,7,8 and 9). Total outcome: 8*8*8*8*1*1*1
Please help!



Manager
Joined: 24 Mar 2010
Posts: 71

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
14 Aug 2014, 18:38
gbascurs wrote: Hi! I have a question here. What does is wrong if we do this in this way? Outcome wanted/Total outcome. This means:
Outcome wanted: 4*4*8*8*1*1*1. I have in the first and in the second digit, 4 possibles numbers (just primes). For the third and fourth digit are 8 possible numbers (2,3,4,5,6,7,8 and 9). Total outcome: 8*8*8*8*1*1*1
Please help! Hey gbascurs, The question ask "What is the probability that the phone number contains at least two prime digits?". At least mean: 2, 3, or 4 primes digits appears in the phone number. You only include one case. Moreover, the two primes can be in the third and fourth digit, not just in the first and second digit. Hope it clears.
_________________
Start to fall in love with GMAT <3



Intern
Joined: 25 Dec 2012
Posts: 16

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
14 Aug 2014, 19:35
LucyDang wrote: gbascurs wrote: Hi! I have a question here. What does is wrong if we do this in this way? Outcome wanted/Total outcome. This means:
Outcome wanted: 4*4*8*8*1*1*1. I have in the first and in the second digit, 4 possibles numbers (just primes). For the third and fourth digit are 8 possible numbers (2,3,4,5,6,7,8 and 9). Total outcome: 8*8*8*8*1*1*1
Please help! Hey gbascurs, The question ask "What is the probability that the phone number contains at least two prime digits?". At least mean: 2, 3, or 4 primes digits appears in the phone number. You only include one case. Moreover, the two primes can be in the third and fourth digit, not just in the first and second digit. Hope it clears. Hi LucyDang, Why I am trying to do now is: Probability of 2 primes = 4*4*8*8*1*1*1 /8*8*8*8*1*1*1 + Probability of 3 primes = 4*4*4*8*1*1*1 /8*8*8*8*1*1*1 + Probability of 4 primes = 4*4*4*4*1*1*1 /8*8*8*8*1*1*1 Probability = 7/16 I cannot see where is the mistake. Thanks!!



Manager
Joined: 24 Mar 2010
Posts: 71

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
14 Aug 2014, 23:58
gbascurs wrote: Hi LucyDang,
Why I am trying to do now is:
Probability of 2 primes = 4*4*8*8*1*1*1 /8*8*8*8*1*1*1 + Probability of 3 primes = 4*4*4*8*1*1*1 /8*8*8*8*1*1*1 + Probability of 4 primes = 4*4*4*4*1*1*1 /8*8*8*8*1*1*1 Probability = 7/16
I cannot see where is the mistake. Thanks!!
Hey gbascurs, There are overlap/incorrect calculation here: Probability of 2 primes = 4*4*8*8*1*1*1 /8*8*8*8*1*1*1 > 4*4*8*8*1*1*1: there are 4 primes each placed in 3rd and 4th digit Probability of 3 primes = 4*4*4*8*1*1*1 /8*8*8*8*1*1*1 > 4*4*4*8*1*1*1: there are 4 primes placed in 4th digit. You have to calculate the case in which same two primes appear, then you need to subtract the primes from the total numbers. It takes lots of time to do so, so please use the P(desire) = 1P(opposite) to get the correct answer under time pressure.
_________________
Start to fall in love with GMAT <3



Intern
Joined: 03 May 2011
Posts: 4

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
17 Dec 2014, 04:50
actually, 1 is neither prime nor composite number, so, the single digit prime numbers are 2, 3, 5, 7. (2 is the only even prime number).



Intern
Joined: 28 Dec 2015
Posts: 37

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
17 Jul 2016, 08:15
stne wrote: Hi
Looking for some assistance with this question , please . XXXX(1}{1}{1} X can be a prime number or non prime number Prime number:2,3,5,7 Non prime4,6,8,9(1 is already taken) Probability(X is a Prime number)=4/8=1/2 Probability(X is a nonprime number)=4/8=1/2 So,Atleast 2 prime numbers=P P NP NP=4!/2!2!*1/2*1/2*1/2*1/2=6/16 Three prime numbers and one Non prime=P P P NP=4!/3!*1//2^4=4/16 All prime=PPPP=1/16 Total=11/16. Remember that its a telelphone number,so different arrangements give you different numbersame goes for codes,passwords,words..



Board of Directors
Status: Emory Goizueta Alum
Joined: 18 Jul 2015
Posts: 3598

John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
17 Jul 2016, 08:50
Ashishsteag wrote: stne wrote: Hi
Looking for some assistance with this question , please . XXXX(1}{1}{1} X can be a prime number or non prime number Prime number:2,3,5,7 Non prime4,6,8,9(1 is already taken) Probability(X is a Prime number)=4/8=1/2 Probability(X is a nonprime number)=4/8=1/2 So,Atleast 2 prime numbers=P P NP NP=4!/2!2!*1/2*1/2*1/2*1/2=6/16 Three prime numbers and one Non prime=P P P NP=4!/3!*1//2^4=4/16 All prime=PPPP=1/16 Total=11/16. Remember that its a telelphone number,so different arrangements give you different numbersame goes for codes,passwords,words.. Can you please explain me why you have multiplied with 4!/2!2!? We do have 2 primes but they could be different, right? So, how are we sure they are same?
_________________
My LinkedIn abhimahna.  My GMAT Story: From V21 to V40  My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeGMAT Club Inbuilt Error Log Functionality  View More  Best Reply Functionality on GMAT Club!New Visa Forum  Ask all your Visa Related Questions  here  Have OPT questions?  Post them here. Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.  Blog: Subscribe to Question of the Day BlogNew! Executive Assessment (EA) Exam  All you need to know!



Intern
Joined: 28 Dec 2015
Posts: 37

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
17 Jul 2016, 09:23
abhimahna wrote: Ashishsteag wrote: stne wrote: Hi
Looking for some assistance with this question , please . XXXX(1}{1}{1} X can be a prime number or non prime number Prime number:2,3,5,7 Non prime4,6,8,9(1 is already taken) Probability(X is a Prime number)=4/8=1/2 Probability(X is a nonprime number)=4/8=1/2 So,Atleast 2 prime numbers=P P NP NP=4!/2!2!*1/2*1/2*1/2*1/2=6/16 Three prime numbers and one Non prime=P P P NP=4!/3!*1//2^4=4/16 All prime=PPPP=1/16 Total=11/16. Remember that its a telelphone number,so different arrangements give you different numbersame goes for codes,passwords,words.. Can you please explain me why you have multiplied with 4!/2!2!? We do have 2 primes but they could be different, right? So, how are we sure they are same? Unless mentioned in the question that repetition is not allowed or different digits have to be used,we should not assume anything on our own. Then,it is clearly mentioned in the question that last three digits are 1,so you have to fix the number 1 and 0 is not used.So,we are left with 8 digits. There can be numbers such as 2244 or say 3366 etc of the format P P NP NP.It's not necessary that they have to be different.It's nowhere mentioned in the question.So,if you have 2244how many ways can you arrange it4!/2!2!=6 ways (2 is repeated 2 times and 4 is repeated 2 times),so divide it by the number of possible arrangement of the number to avoid duplicate numbers.For example 2244 can be written as 2424 2442 4242 4422 4224 2244 6 possible ways. 4!/2!2! means the arrangement of P P NP NP in which 2 objects are the same(prime numbers) and 2 Non prime numbers are the same.If you wouldn't divide it by 2! and 2!,there will be duplicate arrangements. Its the same as arrangement of say word BANANA=you have 6 lettersso they can be arranged in 6! ways/3!(letter A)2!(letter N)



Senior Manager
Joined: 29 Jun 2017
Posts: 411
GPA: 4
WE: Engineering (Transportation)

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
30 Aug 2017, 08:44
ANSWER IS B
Prime is P no Prime is X P(prime) = P(no prime) = 4/8 =0.5 PPPP111___________4!/4! x (0.5)^4 PPPX111___________4!/3! x (0.5)^4 PPXX111___________4!/2!2! x (0.5)^4 Summation = (0.5)^4 { 1+4+6}= 11/16 = Option B



Intern
Joined: 19 Dec 2017
Posts: 7

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
01 Feb 2018, 01:46
Total number of ways in which remaining 4 places can be filled from 8 digits = 8 x 8 x 8 x 8 2 Prime (from 4 prime nos), 2 non prime (from 4 non prime nos) = 4^4 x 4C2 3 Prime, 1 non prime = 4^4 x 4C3 4 Prime, 0 non prime = 4^4 x 4C4 Probability = 4^4(4C2+4C3+4C4)/8^4 = 11/16



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11047
Location: United States (CA)

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
02 Feb 2018, 11:17
scaredshikless wrote: John wrote a phone number on a note that was later lost. John can remember that the number had 7 digits, the digit 1 appeared in the last three places and 0 did not appear at all. What is the probability that the phone number contains at least two prime digits?
A. 15/16 B. 11/16 C. 11/12 D. 1/2 E. 5/8 We know that the singledigit numbers that are primes are 2, 3, 5, and 7. Since the last three digits are all 1’s, we only have to deal with the first 4 digits, in which none of them is 0 (and we are also going to assume that none of the first 4 digits is 1). Thus, the probability that the first 4 digits are all primes (where each digit can be 2 to 9, inclusive) is: 4/8 x 4/8 x 4/8 x 4/8 = (1/2)^4 = 1/16 The probability that exactly 3 of the first 4 digits are primes is: (4/8 x 4/8 x 4/8 x 4/8) x 4C3 = (1/2)^4 x 4 = 4/16 Notice that the last factor 4C3 is the number of ways one can arrange 3 prime digits in 4 spots. The probability that exactly 2 of the first 4 digits are primes is: (4/8 x 4/8 x 4/8 x 4/8) x 4C2 = (1/2)^4 x 6 = 6/16 Thus, the probability that the phone number contains at least two prime digits is: 1/16 + 4/16 + 6/16 = 11/16 Answer: B
_________________
5star rated online GMAT quant self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews



Intern
Joined: 12 Jul 2017
Posts: 32

Re: John wrote a phone number on a note that was later lost
[#permalink]
Show Tags
23 Mar 2018, 08:42
1 can't be in any of the 4 remaining spots. So we have: 2,3,5,7, 4,6,8 and 9. total number of arrangements of 8 numbers in 4 slots is 8*8*8*8=8^4 for two primes with the possibility of repeating numbers is 4*4*4*4 (first two fours are for the primes and the second one is for the non primes) for three primes and four primes we have 4*4*4*4. However, the three can be arranged as follows: PP(NP)(NP): 4!/(2!2!)=6 PPP(NP): 4!/3!=4 PPPP: 4!/4!=1
4^4/8^8=4^4/(2^4*4^4)=1/16 Adding 6,4 and 1 and multiplying by their probability we get 11/16.




Re: John wrote a phone number on a note that was later lost
[#permalink]
23 Mar 2018, 08:42



Go to page
1 2
Next
[ 21 posts ]

