Question

The local weather forecaster says she can predict whether it will rain with 80% accuracy which is equivalent to a 0.8 chance of being correct. If she forecasts rain 160 times, how many of these times would you expect she is wrong?

Answer 1

You should expect her to be wrong 32 times.

Explanation:

For each forecast that she makes, there are only two possible outcomes. Either she is correct, or she is not. The probability of she being correct on a forecast is independent of other forecasts. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

`E(X) = np`

0.8 chance of being correct.

So 1 - 0.8 = 0.2 change of being wrong, which means that
`p = 0.2`

160 forecasts:

This means that
`n = 160`

How many of these times would you expect she is wrong?

`E(X) = np = 160*0.2 = 32`

You should expect her to be wrong 32 times.