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Probability

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by hey_thr67 » Fri Jun 08, 2012 3:55 am
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 ½

OA is E
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by Anurag@Gurome » Fri Jun 08, 2012 4:05 am
hey_thr67 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?
Without any restriction, each of the 10 digits can go to any of the 5 places. Hence, total number of possible passwords = 10^5

With the restriction mentioned we are limited only with 0, 2, 3, 5, and 7. Each of this five digits can go to any of the 5 places. Hence, total number of restricted outcome = 5^5

Hence, required probability = (5^5)/(10^5) = (5/10)^5 = (1/2)^5 = 1/32

The correct answer is A.
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by sam2304 » Fri Jun 08, 2012 4:06 am
Are you sure the OA is E ?

total number of combinations = 10^5
total allowed combinations with prime numbers and 0 = 5^5

Prob = 5^5/2^5*5^5 = 1/2^5 = 1/32

IMO A.
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by hey_thr67 » Fri Jun 08, 2012 6:39 am
My Bad... OA is indeed A. I committed the mistake by not counting 0 at 10 thousand's digit.
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