The probability that a car fails its yearly inspection is 0.4. Suppose that any two cars are considered statistically independent in terms of whether they pass or fail inspection. What is the probability that two randomly selected cars both fail inspection? Give your answer to 2 decimal places.

The probability that a car fails its yearly inspection is 0.4. Suppose that any two cars are considered statistically independent in terms of whether they pass or fail inspection. What is the probability that two randomly selected cars both fail inspection? Give your answer to 2 decimal places.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Expert Solution

Step 1: Introduce the given information

Given the probability that a car fails its yearly inspection is 0.4.

That is, Probability of success, p = 0.4

Sample size, n = 2

Let X be a random variable represents the number of car fails its inspection.

Using formula,

$P left parenthesis X equals r right parenthesis equals C presuperscript n subscript r cross times left parenthesis p right parenthesis to the power of r cross times left parenthesis 1 minus p right parenthesis to the power of n minus r end exponent$

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