Answer: [tex]\dfrac{1}{59049}[/tex]
Step-by-step 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
[tex](9)^5=59049[/tex]
Then , the probability that the choosen pin code is correct is given by :-
[tex]\dfrac{1}{59049}[/tex]
The probability of Geometric distribution formula :
[tex]P(X=x)=(1-p)^{x-1}p[/tex], 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 :-
[tex]P(X=1)=(1-\dfrac{1}{59049})^{1-1}(\dfrac{1}{59049})=\dfrac{1}{59049}[/tex]
