Question

A weather forecast predicts a 25% probability of thunderstorms for tomorrow and a 10% probability of thunderstorms and hail. What is the probability that there is hail tomorrow given that there are thunderstorms?

Answer 1

`P(B | A)=0.4=40\%`

Explanation:

Call A to the event in which there are electrical storms.

Call B the event in which there is hail.

Then, by definition.

The Probability of B given A is:

`P(B | A)=(P(B\ and\ A))/(P(A))`

We know that:

`P(B\ and\ A)= 10\%=0.1\\\\P(A) = 25\%=0.25`

Therefore

`P(B | A)=(0.1)/(0.25)`

`P(B | A)=0.4=40\%`