Answer to Question #264113 in Statistics and Probability for Nathan

Question

In a coastal South African town, it is rainy on one fifth of the days. If it is rainy, the probability of heavy traffic is 0.75. On the other hand, the probability of heavy traffic reduces to 0.125 if it is not rainy. A random day has heavy traffic. What is the probability that it rained?

Answer 1

$P(rained)=\frac{0.2*0.75}{0.2*0.75+(1-0.2)*0.125}=\frac{0.15}{0.25}=0.6.$