Question

A family picnic scheduled for tomorrow will be postponed if it is either cloudy or rainy. If the probability that it will be cloudy is .40, the probability that it will be rainy is .30, and the probability that it will be both rainy and cloudy is .20, what is the probability that the picnic will not be postponed?

Answer 1

0.50

Explanation:

Let A represent the probability that it will be cloudy

Let B represent the probability that it will be rainy

P(A) = 0.40

P(B) = 0.30

P(A and B) = 0.20

For non mutually exclusive events the probability of event A or B is

P(A or B) = P(A) + P(B) - P(A and B)

= 0.40 + 0.30 - 0.20

= 0.50

There is a 50% probability that the picnic will be postponed. Therefore the probability that the picnic will not be postponed is equals 1 - P(A and B)

= 1 - 0.50

= 0.50 or 50%