Question

A weather forecaster predicts that their is 50% chance of rain on Saturday and a 40% chance of rain on Sunday. If these probabilities are correct, what is the probability that it will rain both days?

20% 45% 10% 90%

Answer 1

20%

Explanation:

The events are independent (the probability of one does not affect the probability of the other). Therefore:

P(A and B) = P(A) P(B)

P(A and B) = (0.50) (0.40)

P(A and B) = 0.20

Answer 2

20%

Explanation:

Let A is the event of raining on Saturday and B is the event of raining on Sunday,

According to the question,

P(A) = 50% = 0.50,

P(B) = 40% = 0.40,

Thus, the probability of raining in both days,

`P(A\cap B) = P(A)* P(B)` ( ∵ events A and B are independent i.e. the chance of raining on Sunday does not effect by raining on Saturday or vice versa ),

By substituting the values,

`P(A\cap B) = 0.50* 0.40 = 0.20 = 20%`

Hence, FIRST OPTION is correct.