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A password of a computer used five digits where they are fro

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aniketb
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A password of a computer used five digits where they are fro [#permalink] New post   06 May 2014, 07:23
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A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2
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A
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Re: A password of a computer used five digits [#permalink] New post   06 May 2014, 07:47
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We have five digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 =1/32 (A)
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Re: A password of a computer used five digits [#permalink] New post   06 May 2014, 08:29
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aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2

How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...


A 5-digit number cannot have 0 as its first digit while a 5-digit password can. For example, a password can be 00000.

Does this make sense?
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Re: A password of a computer used five digits where they are fro [#permalink] New post   28 Jun 2014, 04:58
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maggie27 wrote:
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ? :oops:


For two reasons.

1. 10C5 gives the number of groups of 5 possible out of 10 when the order of the selection is not important. In passwords the order of the numbers is important

2. 10C5 gives 5 different numbers out of 10, while the numbers in passwords can be repeated.

Thus the total number of passwords is 10*10*10*10*10 (10 options for each of the 5 digits we have in the password).

Hope it's clear.
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Re: A password of a computer used five digits [#permalink] New post   06 May 2014, 07:55
How can we have probability for 1st digit as 5/10, if 0 gets selected at first place its no longer a 5 digit number...
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Re: A password of a computer used five digits where they are fro [#permalink] New post   06 May 2014, 23:15
oh o..missed that. Thanks Bunuel.
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Re: A password of a computer used five digits where they are fro [#permalink] New post   27 Jun 2014, 16:36
For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ? :oops:
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Re: A password of a computer used five digits where they are fro [#permalink] New post   28 Jun 2014, 07:13
Thank You so much Bunuel :)
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Re: A password of a computer used five digits where they are fro [#permalink] New post   29 Sep 2014, 22:43
I got stuck looking for combination approach here, it was tempting. After shifting direct probability easily found that
it is just
(1/2)^5=1/32

i thing direct method is better anyway
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Re: A password of a computer used five digits where they are fro [#permalink] New post   24 Feb 2016, 07:33
good question.. but it should be given that the numbers may repeat.
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Re: A password of a computer used five digits where they are fro [#permalink] New post   10 May 2018, 10:42
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aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


The total number of ways to select 5 digits to form a 5-digit password is 10^5. The number of ways to select the 5 digits that are either a prime (2, 3, 5, 7) or zero is 5^5. Therefore, the probability is 5^5/10^5 = (5/10)^5 = (1/2)^5 = 1/32.

Answer: A
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Re: A password of a computer used five digits where they are fro [#permalink] New post   22 May 2018, 05:03
How do we know whether the repetition of ghe digits are allowed or not.
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Re: A password of a computer used five digits where they are fro [#permalink] New post   22 May 2018, 05:38
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lincy93 wrote:
How do we know whether the repetition of ghe digits are allowed or not.


Restriction that the repetition is not allowed is not given so we can assume that it's allowed though proper GMAT question would make this issue clearer.
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Re: A password of a computer used five digits where they are fro [#permalink] New post   18 Dec 2018, 23:21
Total possible ways of designing a password = 105ways.
No of 0’s and prime no between 0 and 9 = 5 (1,2,3,5,7)
So, The probability of favorable arrangements = 105/55 = 1/32.
Hence, a is the answer.
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Re: A password of a computer used five digits where they are fro [#permalink] New post   16 May 2019, 09:04
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


total such no
0,2,3,5,7
5/10 ; 1/2
for 5 digits; (1/2)^5 = 1/32
IMOA
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Re: A password of a computer used five digits where they are fro [#permalink] New post   20 Sep 2019, 11:14
aniketb wrote:
A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

A. 1/32
B. 1/16
C. 1/8
D. 2/5
E. 1/2


SOLUTION 1 (CHOICES)

\(digits:0,1,2,3,…9=10\)
\(choices:0,2,3,5,7=5\)
\(favorable.outcomes:5^5\)
\(total.outcomes:10^5\)
\(p(zeros.primes)=5^5/10^5=1/32\)

Answer (A)

SOLUTION 2 (CASE BY CASE)

\(primes:2,3,5,7 = 4\)
\([00000:only.zero]…1^5•5!/5!=1\)
\([0000P:zeros.prime]…1^4•4•5!/4!=4•5=20\)
\([000PP:zeros.primes]…1^3•4^2•5!/3!2!=16•10=160\)
\([00PPP:zeros.primes]…1^2•4^3•5!/2!3!=64•10=640\)
\([0PPPP:zero.primes]…1•4^4•5!/4!=256•5=1280\)
\([PPPPP:primes]…4^5•5!/5!=1024\)
\([XXXX:any]…10^5=100,000\)
\(favorable.outcomes=1+20+160+640+1280+1024=3125\)
\(total.outcomes=100000\)
\(p(zeros.primes)=3125/100000=1/32\)

Answer (A)
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Re: A password of a computer used five digits where they are fro [#permalink] New post   15 Sep 2023, 23:33
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Re: A password of a computer used five digits where they are fro [#permalink]
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