Question

A thief steals an atm card and must randomly guess the correct three digit pin code from a 9 key keypad repetition of digits is allowed. That is the probability of a correct guess in the first try?

Answer 1

Answer:

1/729

Step-by-step explanation:

Assuming that the probabilities of each digit in the pin is independent from the other digits, the answer to this question can be calculated. There are total of 9 digits, out of which 1 digit is correct. This is true for all the three digits. So the probability of choosing the correct digit in the first place in the first try will be 1/9. Since this is true for the rest of the digits as well and they are independent, we can safely multiply the probabilities. So P(Correct Guess in the first try) = 1/9 (first place) * 1/9 (second place) * 1/9 (third place) = $1/9^3$ = 1/729. So the correct answer is 1/729!!!