Question

The probability of rain on a day of the year selected at random is 0.25 in a certain city. The local weather forecast is correct 60% of the time when the forecast is rain and 80% of the time for other forecasts. What is the probability that the forecast on a day selected at random is correct

Answer 1

Answer: 0.75

Explanation:

Let R be the event that it will rain, then R' will be the event that it will not rain

Let C be the event thatt forecast is correct.

Given: P(R)=0.25 P(R') =1-0.5=0.75

P(C|R)=0.60 P(C|R')=0.80

By law of total probability, we have

P(C)= P(C|R) × P(R) + P(C|R') ×P(R')

i.e. P(C) = 0.60×0.25+0.80×0.75

=0.75

Hence, the probability that the forecast on a day selected at random is correct = 0.75