Question

A thief steals an ATM card and must randomly guess the correct four​-digit pin code from a 9​-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first​ try?

Answer 1

Answer:
`(1)/(59049)`

Explanation:

The number of keys on the keypad = 9

The number of digits in the required pin code = 4

If repetition is allowed then , the number of possible codes will be

`(9)^5=59049`

Then , the probability that the choosen pin code is correct is given by :-

`(1)/(59049)`

The probability of Geometric distribution formula :

`P(X=x)=(1-p)^(x-1)p`, where p is the probability of success and x is the number of attempt.

Using geometric probability , the probability of a correct guess on the first​ try is given by :-

`P(X=1)=(1-(1)/(59049))^(1-1)((1)/(59049))=(1)/(59049)`