L3 · Equally likely outcomes and experiments

Learning goal

“I can tell when outcomes are equally likely, and find the likelihood of an event by counting: favourable outcomes / possible outcomes. I can also compare that likelihood with the relative frequency from actually running the experiment.”

Equally likely — outcomes that have the same chance of happening, like the six faces of a fair die.

Favourable outcome — an outcome that counts as a "success" for the event you are asking about, like rolling an even number.

Possible outcomes — every outcome that could happen, counted one by one - the six faces, the eight sectors, the twelve counters.

Fair — a device is fair when its outcomes are equally likely: a balanced die, a spinner with equal sectors.

Worked example

A fair die has faces 1, 2, 3, 4, 5, 6 - six possible outcomes, all equally likely. Step 1: Event: roll an even number. The favourable outcomes are 2, 4, 6 - that is 3 favourable. Step 2: Likelihood = favourable / possible = 3/6. Step 3: Simplify: 3/6 = 1/2. (As a relative-frequency-style fraction: the even faces are half of all the faces.)

Check yourself — explain it

The denominator in 3/6 counts...

Paired problem — example still visible

What is the likelihood of rolling a number greater than 4 on a fair die? -> 2/6 = 1/3 (the favourable faces are 5 and 6)

Faded completion — last step is yours

"Likelihood of rolling exactly a 5: ___/6." -> 1 (1/6)

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