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?

You should expect her to be wrong 32 times.

Step-by-step 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:

0.8 chance of being correct.

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

160 forecasts:

This means that

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

You should expect her to be wrong 32 times.