Question

Each day, a weather forecaster predicts whether or not it will rain. For 80% of rainy days, she correctly predicts that it will rain. For 90% of non-rainy days, she correctly predicts that it will not rain. Suppose that 10% of days are rainy and 90% are non-rainy.
What proportion of the forecasts are correct?

Answer 1

Answer: Our required proportion of the forecasts are correct is 89%.

Step-by-step explanation:

Since we have given that

Percentage of rainy days she correctly predicts that it will rain = 80%

Percentage of non rainy days, she correctly predicts that it will not rain = 90%

Percentage of rainy days = 10%

Percentage of non rainy  days = 90%

So, Probability of forecasts are correct is given by

P(rainy day).P(correctly predicted) + P(non rainy day) .P(correctly predicted)

$0.1\times 0.8+0.9\times 0.9\\\\=0.08+0.81\\\\=0.89\\\\=89\%$

Hence, our required proportion of the forecasts are correct is 89%.