Question

a thief steals an atm card and must randomly guess the correct three - digit pin code from a 7 - 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 7 ways since there are 7 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 $7\times7\times7=7^{3}=343$.

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 outcomes (343). So the probability is $\frac{1}{343}$.

Answer:

The number of possible codes is 343. The probability of a correct guess on the first try is $\frac{1}{343}$.