L4 · Predicting likelihood from relative frequency

Learning goal

“I can use a relative frequency from past trials to predict about how many times an outcome will happen in a future set of trials - and I know a prediction is an estimate, not a promise.”

Predict — to use past results to say what will probably happen next.

Estimate — a sensible answer that is close but not exact; predictions from relative frequency are estimates.

Expected count — the predicted number of times an outcome will happen in a future set of trials: relative frequency x future trials.

Likely / unlikely — words comparing chances: an outcome with a bigger relative frequency is more likely; one close to 0 is unlikely.

Worked example

In practice, Ana made 18 of her 24 free throws. Step 1: Find her relative frequency: 18/24 = 3/4 (or 75%). Step 2: To predict her next 20 shots, take that share of 20: 3/4 x 20 = 15. Step 3: Say it honestly: she will make about 15 of the next 20. The relative frequency describes the share, and the share is applied to the new number of trials.

Check yourself — explain it

We multiply the relative frequency by the future trials because...

Paired problem — example still visible

A spinner landed on the star sector 30 times in 50 spins. Predict the number of star landings in the next 100 spins. -> Relative frequency 30/50 = 3/5; 3/5 x 100 = 60, so about 60 star landings

Faded completion — last step is yours

"Relative frequency = 1/4. In 80 future trials, the expected count is 1/4 x 80 = ___." -> 20

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