Question

a thief steals an atm card and must randomly guess the correct three - digit pin code from a 10 - key keypad. repetition of digits is allowed. what is the probability of a correct guess on the first try? the number of possible codes is . (type an integer or fraction. simplify your answer.)

Explanation:

Step1: Calculate number of possibilities for each digit

Each digit of the 3 - digit PIN can be chosen in 10 ways (since there are 10 keys on the keypad and repetition is allowed).

Step2: Use the multiplication principle

The total number of possible 3 - digit PINs is the product of the number of possibilities for each digit. So the number of possible codes is $10\times10\times10=10^3 = 1000$.

Step3: Calculate the probability

The probability of a correct guess on the first try is the ratio of the number of correct outcomes (1) to the number of total possible outcomes. The probability $P=\frac{1}{1000}$.

Answer:

The number of possible codes is 1000. The probability of a correct guess on the first try is $\frac{1}{1000}$.