A tire manufacturer claims that the probability of its XLT t

A tire manufacturer claims that the probability of its XLT tire lasting 50,000 miles or more is 0.80. If three XLT tires are installed on a car what is the probability that all three will last 50,000 miles or more?

Solution

let X be the random variable denoting the number of XLT tires lasting 50,000 miles or more out of 3 tires

now the probability of XLT tire lasting 50,000 miles or more is 0.80

so X~Bin(3,0.8)

here we need to find P[X=3]=³C₃0.8³=0.512 [answer]