Question

On any given day, the probability that it is raining when Randy goes to class is 0.2. If it is raining, the probability that Randy is on time to class is 0.7. If it is not raining, the probability that Randy is on time to class is 0.90. What is the probability that it is raining given that Randy is late to class

Answer 1

The probability that is raining given that Randy is late to class is P(R|L)=0.175.

Explanation:

We can apply the Bayes theorem to solve this question.

Being

L: Randy is late to class

R: It is raining

nL: Randy is on time to class

nR: It is not raining

We know:

P(L | R)= 1-0.7=0.3

P(L | nR) = 1-0.9=0.1

P(R) = 0.2 (probability of Randy going to class given that is raining)

P(nR) = 0.8

We have to calculate P(R | L): probability that is raining given that Randy is late to class.

If we apply the Bayes theorem, we have:

`P(R | L)=(P(L|R)P(R)+P(L|nR)P(nR))/(P(L|R)+P(L|nR))=(0.3\cdot0.2+0.1\cdot0.1)/(0.3+0.1)\\\\\\P(R | L)=(0.06+0.01)/(0.4)=(0.07)/(0.4)=0.175`

The probability that is raining given that Randy is late to class is P(R|L)=0.175.