Question

a thief steals an atm card and must randomly guess the correct three - digit pin code from a 8 - 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 8 ways since repetition is allowed and there are 8 keys on the keypad.

Step2: Use the multiplication principle

The total number of possible 3 - digit pins is the product of the number of choices for each digit. So the number of possible codes is $8\times8\times8=8^{3}=512$.

Step3: Calculate the probability

The probability of guessing correctly on the first try is the number of correct outcomes (1) divided by the number of total possible outcomes. The probability $P=\frac{1}{512}$.

Answer:

The number of possible codes is 512. The probability of a correct guess on the first try is $\frac{1}{512}$.