Expected Outcomes

In a Nutshell

The expected number of times an event occurs is probability×number of trials\text{probability} \times \text{number of trials}.

If you know the probability of an event, you can predict how many times it should happen over many trials. This is called the expected outcome (or expected frequency).

Expected frequency=P(event)×n\text{Expected frequency} = P(\text{event}) \times n

where nn is the number of trials. For example, if you roll a fair die 60 times, the expected number of sixes is:

16×60=10\frac{1}{6} \times 60 = 10

This does not mean you will get exactly 10 sixes — it is the long-run average you would expect.

Use the simulator below to see how actual results compare to the expected frequency (shown by the dashed line).

Frequency experiment simulator A bar chart that grows as trials are run, showing the relative frequency of each outcome approaching the theoretical probability. Relative frequency 0.00 0.25 0.50 0.75 1.00

Trials: 0

Watch it work

Question: A spinner has a 38\frac{3}{8} chance of landing on red. If it is spun 200 times, how many times would you expect it to land on red?

Have a go

Q1. A coin is flipped 300 times. How many heads would you expect?

Q2. The probability of a biased die landing on 3 is 0.20.2. It is rolled 500 times. How many threes would you expect?

Q3. A bag contains 2 red and 3 blue counters. A counter is picked at random, its colour recorded, then returned. This is done 80 times. How many times would you expect to pick blue?

Q4. After 1000 rolls of a fair die, Jamie got 185 sixes. Is this close to the expected number? Explain.