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 343 (type an integer or fraction. simplify your answer.) the probability that the correct code is given on the first try is (type an integer or fraction. simplify your answer.)

Explanation:

Step1: Calculate total number of possibilities

Since repetition of digits is allowed and there are 7 - key keypad for each of the 3 - digit pin code, by the multiplication principle, the total number of possible codes is $7\times7\times7 = 7^{3}=343$.

Step2: Calculate probability

The probability $P$ of a correct guess on the first try is the ratio of the number of favorable outcomes (which is 1, since there is only 1 correct code) to the number of total possible outcomes. So $P=\frac{1}{343}$.

Answer:

$\frac{1}{343}$