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?
Accepted Solution
A:
Answer: [tex]\dfrac{1}{59049}[/tex]Step-by-step explanation:The number of keys on the keypad = 9The number of digits in the required pin code = 4If 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]