Question

Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is ten percent. However, in any year, the probability of water rationing is five percent.

Which of the following is true?
a. 0.01
b. 0.05
c. 0.30
d. 0.02

Answer 1

the correct option is d. 0.02

Explanation:

We have the following events:

x: A drought occurd

y: Water rationing.

Therefore, according to the plaster we have:

P [x] = 0.20

P [y | x] = 0.10

Now P [it is a drought and water rationing happens] =

P [x n y] = P [y | x] * P [x] = 0.10 * 0.20 = 0.02

Which means that the correct option is d. 0.02