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

Since repetition of digits is allowed and there are 7 - key keypad, for each of the three - digit pin code, there are 7 possibilities.

Step2: Use the counting principle

The total number of possible three - digit pin codes 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 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 $P=\frac{1}{343}$.

Answer:

$\frac{1}{343}$