Expected Outcomes

This lesson covers how to calculate the expected number of times an event will occur, given a probability and a number of trials. This is a key topic in the AQA GCSE Mathematics specification and frequently appears in exam questions combining probability with number work.

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What Are Expected Outcomes?

If you know the probability of an event and the number of times an experiment is repeated, you can calculate the expected frequency (the number of times you expect the event to happen).

Expected frequency = probability x number of trials

This is sometimes called the expected number of outcomes or expected value.

Worked Example 1

A fair coin is flipped 200 times. How many times would you expect to get heads?

• P(heads) = 1/2 = 0.5
• Number of trials = 200

Expected frequency = 0.5 x 200 = 100

You would expect to get heads 100 times.

Exam Tip: The expected frequency is a theoretical prediction. In practice, you are unlikely to get exactly 100 heads in 200 flips — but it is the best estimate based on the given probability.

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Calculating Expected Frequency from a Probability Table