Question

the access code for a garage door consists of three digits. each digit can be any number from 1 through 9, and each digit can be repeated. complete parts (a) and (b). (a) what is the probability of randomly selecting the correct access code on the first try? (b) what is the probability of not selecting the correct access code on the first try? (a) what is the probability of randomly selecting the correct access code on the first try? the probability of randomly selecting the correct access code is (round to three decimal places as needed.)

Explanation:

Step1: Calculate total number of possible codes

Since each digit can be from 1 - 9 (9 choices) and there are 3 digits. By the fundamental counting principle, the total number of access codes is \(9\times9\times9=9^{3}=729\).

Step2: Calculate probability of correct code

The probability \(P\) of an event is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). There is 1 correct code. So \(P=\frac{1}{729}\approx0.001\).

Answer:

\(0.001\)