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?

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)

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

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8