Question

Studies indicate that there is a 65% chance that the Hope River will overflow its banks if there is heavy rainfall. The studies further indicated that the probability that the river will overflow its banks if there is no heavy rainfall is 0.15. If the probability of heavy rain for this season is 0.75;

What is the probability that the Hope River will overflow its banks this season?

Answer 1

Explanation:

We can use the law of total probability to calculate the probability that the Hope River will overflow its banks this season:

P(overflow) = P(overflow | heavy rain) x P(heavy rain) + P(overflow | no heavy rain) x P(no heavy rain)

From the problem statement, we are given:

P(overflow | heavy rain) = 0.65 (the probability of overflow given heavy rain)

P(overflow | no heavy rain) = 0.15 (the probability of overflow given no heavy rain)

P(heavy rain) = 0.75 (the probability of heavy rain)

We can find P(no heavy rain) as:

P(no heavy rain) = 1 - P(heavy rain) = 1 - 0.75 = 0.25

Substituting these values, we get:

P(overflow) = 0.65 x 0.75 + 0.15 x 0.25

= 0.4875 + 0.0375

= 0.525

Therefore, the probability that the Hope River will overflow its banks this season is 0.525, or 52.5%.