Question

A weather forecaster claimed the chance of rain next week on Monday is 50% and the chance it rains on Tuesday is 80%. Is the probability that it rains next

Monday and Tuesday equal to 40%?
O Yes, because the chance of rain on Monday and the chance of rain on Tuesday are independent.
O No, because the chance of rain on Monday and the chance of rain on Tuesday are not independent.
O No, because the chance of rain Monday and the chance of rain Tuesday are not mutually exclusive.
O Yes, because the chance of rain on Monday and the chance of rain on Tuesday are mutually exclusive,

Answer 1

A: Yes, because the chance of rain on Monday and the chance of rain on Tuesday are independent.

Explanation:

We are given;

chance of rain next week on Monday is 50%. Thus;

P(rain next Monday) = 0.5

chance it rains on Tuesday is 80%. Thus;

P(rain next Tuesday) = 0.8

From independent events, we can say that;

P(A and B) = P(A) × P(B)

A and B are independent events because the probability of A doesn't affect B as is the case for rain on Monday and Tuesday given.

Thus;

P(rain on Monday & tuesday next week) = 0.5 × 0.8 = 0.4

This can also be written as 40%

Correct answer is option A since both events are independent