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PS_Probability_800Score

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by farooq » Mon Oct 05, 2009 8:20 pm
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


Correct Answer is A

What can be a simple way to solve this problem.
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Re: PS_Probability_800Score

by Brent@GMATPrepNow » Mon Oct 05, 2009 8:33 pm
farooq 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


Correct Answer is A

What can be a simple way to solve this problem.
Aside: There are 10 possible options (0,1,2,3,4,5,6,7,8,9) for each digit.
5 of the options (0,2,3,5,7) are zero or prime.
So, P(a given digit is zero or prime) = 5/10 = 1/2

A quick way is to look at this as an AND probability.
P(all five digits are zero or prime) = P(1st digit is zero or prime AND 2nd digit is zero or prime AND 3rd digit is zero or prime AND 4th digit is zero or prime AND 5th digit is zero or prime)

This is equal to P(1st digit is zero or prime) x P(2nd digit is zero or prime) x P(3rd digit is zero or prime) x P(4th digit is zero or prime) x P(5th digit is zero or prime)

So, we get 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/32
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by jube » Mon Jun 14, 2010 12:06 pm
Hi,

I think there's one thing wrong with this answer - the first digit canNOT be 0 - since it's a 5 digit no. Therefore, 1st digit probability will be 4/9 and then 2nd, 3rd, 4th & 5th digits will be 1/2 each.

Therefore answer should be 1/36 - which is actually not even there in the options. :\

Can anyone tell me what I'm doing wrong here?

thanks!
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by GMATGuruNY » Mon Jun 14, 2010 12:18 pm
jube wrote:Hi,

I think there's one thing wrong with this answer - the first digit canNOT be 0 - since it's a 5 digit no. Therefore, 1st digit probability will be 4/9 and then 2nd, 3rd, 4th & 5th digits will be 1/2 each.

Therefore answer should be 1/36 - which is actually not even there in the options. :\

Can anyone tell me what I'm doing wrong here?

thanks!
Be careful! Don't make up a restriction that isn't mentioned in the problem. The problem states only that the password will be made up of 5 digits; there is no reason that the first digit cannot be zero.
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by Stuart@KaplanGMAT » Mon Jun 14, 2010 5:57 pm
jube wrote:Hi,

I think there's one thing wrong with this answer - the first digit canNOT be 0 - since it's a 5 digit no.
Hi!

If the question referred to a 5 digit number, you'd be 100% correct in your analysis, since "0" isn't a significant digit in the first spot.

However, in this question we're talking about a 5 digit passcode. Is there any reason why a 5 digit passcode can't start with 0? No, of course not - so in this particular situation, 0 is an acceptable first digit.
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by this_time_i_will » Mon Jun 14, 2010 6:03 pm
password = _ _ _ _ _ (5 digits)
total ways = 10*10*10*10*10 = 10^5. (we have option of picking any one digit from 10 digits)
requireed way = 5*5*5*5*5 = 5^5.(we have option of picking any one digit from 0,2,3,5,7)

so required probability = 5^5/10^5 = 1/2^5 = 1/32
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by jube » Mon Jun 14, 2010 10:50 pm
Stuart Kovinsky wrote:
jube wrote:Hi,

I think there's one thing wrong with this answer - the first digit canNOT be 0 - since it's a 5 digit no.
Hi!

If the question referred to a 5 digit number, you'd be 100% correct in your analysis, since "0" isn't a significant digit in the first spot.

However, in this question we're talking about a 5 digit passcode. Is there any reason why a 5 digit passcode can't start with 0? No, of course not - so in this particular situation, 0 is an acceptable first digit.
Ahh, got it! Thanks Stuart!
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