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marcodonzelli
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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marcodonzelli
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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its E. 50/625 = 2/25

the telephone number is: xxx-xxxxx-ab
we need to find the digits ab:
0, 1, 2, 5, and 7 cannot be in digits ab.
remaining integers 3, 4, 6, 8, and 9 can be chosen for ab.
no of ways the integers can be put in place of ab = 5x5 = 25

prob = 1/25 + 1/25 = 2/25. which is E. i did it via this approach is it correct?

marcodonzelli
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
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i think logically = 1/25 + [24/25 * 1/24] as once we assume a wrong guess he wont repeat it.. he will just have 24 other guesses left
incognito1


Answer should be (E)

5 numbers in each of the last two positions
==> total of 25 2-digit numbers
==> probability of getting it right in one guess = 1/25

Total Probability = P(get it right the first try) + P(get it right the second try)
= 1/25 + [24/25 * 1/25]
= 49/625, closest to (E)
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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 ?

Since Bob remembers the 3-digit area code and next 5 digits of 10 digit telephone number, he has to guess next 2 digits comprising of digits {3,4,6,8,9}.

The probability of selecting the right combination of 2 digits in one attempt = 1/5*5 = 1/25
The probability of NOT selecting the right combination of 2 digits in one attempt = 1 - 1/25 = 24/25

The probability that he will be able to find the correct number in at most 2 attempts = 1/25 + 24/25*1/25 = (25+24)/625 = 49/625

Since there is no option of 49/625, the closest option is 50/625

IMO E
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is it wrong if i do this
1/5*1/5 (1st time correct)+1/5*4/5*1/5*1/5 (2nd digit wrong first time)+4/5*4/5*1/5*1/5 (1st digit wrong first time )+4/5*4/5*1/5*1/5 ( both digit wrong first time)
marcodonzelli
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
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