Question

A mechanic performs MOT tests on cars to see if they are roadworthy, and only 75% of cars pass this test  If 10 cars are tested one day, find the probability that 8 or more cars pass the test.

Answer 1

This is a binomial distribution with $p=0.75, n=10.$

$P(X\ge8)=P(X=8)+P(X=9)+P(X=10)=$

$=C_{10}^8*0.75^8(1-0.75)^2+C_{10}^9*0.75^9(1-0.75)^1+C_{10}^{10}*0.75^{10}(1-0.75)^0=$

$=0.2816+0.1877+0.0563=0.5256.$