Question

the access code for a garage door consists of three digits. each digit can be any number from 1 through 5, 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:

Calculate total possible access codes

Using the Fundamental Counting Principle knowledge point

$$ N = 5 \times 5 \times 5 = 125 $$

Calculate probability of selecting the correct code

Using the Classical Probability knowledge point

$$ P(\text{Correct}) = \frac{1}{125} = 0.008 $$

Calculate probability of not selecting the correct code

Using the Complementary Events knowledge point

$$ P(\text{Incorrect}) = 1 - P(\text{Correct}) = 1 - 0.008 = 0.992 $$

Answer:

Question 1

The probability of randomly selecting the correct access code is <blank>0.008</blank>

Question 2

The probability of not selecting the correct access code is <blank>0.992</blank>