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 1000. (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: Recall probability formula

The probability $P$ of an event is given by $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$.

Step2: Identify favorable and total outcomes

The number of favorable outcomes (correct code) is 1. The total number of possible three - digit codes with 10 choices for each digit (since repetition is allowed) is $10\times10\times10 = 1000$.

Step3: Calculate probability

$P=\frac{1}{1000}$

Answer:

$\frac{1}{1000}$