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 0.001.
(round to three decimal places as needed.)
(b) what is the probability of not selecting the correct access code on the first try?
the probability of not selecting the correct access code is □.
(round to three decimal places as needed.)

Explanation:

Step1: Recall the probability formula

The probability of an event \(A\) is \(P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). The probability of an event not - occurring \(P(\overline{A}) = 1 - P(A)\)

Step2: Use the formula for part (b)

We know from part (a) that \(P(\text{correct code})=0.001\).
Let \(A\) be the event of selecting the correct access code. Then the event of not selecting the correct access code is \(\overline{A}\)
Using the formula \(P(\overline{A})=1 - P(A)\)
Substitute \(P(A) = 0.001\) into the formula: \(P(\overline{A})=1 - 0.001\)

Step3: Calculate the value

\(P(\overline{A})=0.999\)

Answer:

The probability of not selecting the correct access code is \(0.999\)