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

Question

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

dwingrider · Answer

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)

aniketb · Answer

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...

Bunuel · Answer

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?

aniketb · Answer

oh o..missed that. Thanks Bunuel.

maggie27 · Answer

For sure a stupid question but still... why are we not doing a 10C5 here for total possible outcomes ? :oops:

Bunuel · Answer

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.

maggie27 · Answer

Thank You so much Bunuel

Temurkhon · Answer

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

Abhigyanashakuntalam · Answer

good question.. but it should be given that the numbers may repeat.

ScottTargetTestPrep · Answer

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

lincy93 · Answer

How do we know whether the repetition of ghe digits are allowed or not.

Bunuel · Answer

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.

Krabhay · Answer

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.

Archit3110 · Answer

total such no
0,2,3,5,7
5/10 ; 1/2
for 5 digits; (1/2)^5 = 1/32
IMOA

exc4libur · Answer

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 
  …1^5•5!/5!=1 
  …1^4•4•5!/4!=4•5=20 
  …1^3•4^2•5!/3!2!=16•10=160 
  …1^2•4^3•5!/2!3!=64•10=640 
  …1•4^4•5!/4!=256•5=1280 
  …4^5•5!/5!=1024 
  …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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A password of a computer used five digits where they are fro

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