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Re: A telephone number contains 10 digit, including a 3-digit [#permalink]
marcodonzelli wrote:
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 5, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?

A. 1/625
B. 2/625
C. 4/625
D. 25/625
E. 50/625


probability of success in at most 2 attempts =
{Probability of success in 1st attempt} OR {(Probability of failure in 1st attempt) AND (Probability of success in 2nd attempt) }
= {1/25} + {[1-(1/25)] * [1/24]}
=(1/25) + [(24/25) * (1/24)]
= (1/25) + (1/25)
=(2/25)
=(50/625)

Hence Answer : E
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Re: A telephone number contains 10 digit, including a 3-digit [#permalink]
marcodonzelli wrote:
A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 2, 5, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following ?

A. 1/625
B. 2/625
C. 4/625
D. 25/625
E. 50/625


I see a lot of complicated solution to this answer, but here's my answer. Can anyone tell me if my approach is incorrect?

-- 10 digit
-- first 8 known
-- last 2 unknown
--last 2 are not 0,1,2,5, and 7 --> last 2 are 3,4,6,8,9 = 5 possible inputs

To fill two places
_ _
5x5 = 25 ways

1 attempt correct = 1/25
2 attempts correct = 1/25 * 24/25 = 24/625

Therefore, correct in at most 2 attempts = 1/25 + 24/625 = 49/625 = ~50/625
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Re: A telephone number contains 10 digit, including a 3-digit [#permalink]
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