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