Expectation is the amount of times that you expect something to happen. To work out the expectation multiply the probability by the amount of trials.

**Expectation = Probability × the number of trials**

Or you could change the multiplication sign to an of:

**Expectation = Probability of the number of trials**

This is useful if you don’t have your scientific calculator.

**Example 1**

Andrew rolls a dice 320 times. Work out the amount of times you would expect Andrew to roll a 3.

The probability of rolling a 3 is 1/6 and the amount of trials is 320.

So the Expectation = 1/6 × 360 = 60

If you didn’t have a scientific calculator then the expectation can be found by finding 1/6 of 360 which is 60 (do 360 divided by 6)

**Example 2**

The probability that it rains on any particular day is 0.35. Out of the next 40 days, how many rain days can you expect?

The probability that it rains is 0.35 and the number of trials is 40.

Therefore:

Expectation = 0.35 × 40 = 14.

So the amount of times you expect it to rain out of the next 40 days is 14.

**Example 3**

The probability that Thomas spins the colour red on a spinner is 5/7. If Thomas spins the spinner 28 times, work out the amount of times you expect Thomas not to spin the colour red.

First you need to work out the probability of not spinning a red. Do this by taking the probability of spinning a red away from 1.

1 – 5/7 = 2/7

So the probability of not spinning a red is 2/7 and the number of trials is 28.

So the expectation is 2/7 of 28. This is 28 ÷ 7 × 2 = 8.

Or do 2/7 × 28 if you have a scientific calculator.

So the amount of times you expect not to spin a red is 8.