Probability

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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 am; Thanked: 9 times; Followed by:2 members

Probability

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 Â½

OA is E

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Source: Beat The GMAT — Problem Solving | Fri Jun 08, 2012 3:55 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

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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sam2304: Legendary Member; Posts: 1239; Joined: Tue Apr 26, 2011 6:25 am; Thanked: 233 times; Followed by:26 members; GMAT Score:680

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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