Expected Frequency — How Often Over Many Tries (Grade 7)
If you repeat an experiment many times, the expected number of times an event happens is its probability times the number of trials.
Understanding expected frequency
Roll a die 60 times: since P(rolling a 4) = 1/6, you'd expect about 1/6 × 60 = 10 fours. It's an estimate of the long-run count, not a guarantee for any single run.
Seeing it in action
Worked example
Roll a fair die 60 times — expected number of 4s?
P(4) = 1/6. Expected = 1/6 × 60 = 10.
Expected count = probability × number of trials.
A common mistake, and the fix
Expecting exactly the expected count.
Expected frequency is a long-run estimate: 60 rolls of a fair die are expected to give about 10 fours, but a single run of 60 can easily give 7 or 13. The expected number doesn’t have to be a whole number either: 50 rolls give an expected 50 × 1/6, about 8.3 fours.
Try a few
Flip a coin 50 times — expected heads?
1/2 × 50.
Spinner P(gold)=1/4, spun 20 times — expected golds?
¼ × 20.
P(red)=1/3, 30 draws — expected reds?
⅓ × 30.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
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