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Compound probability word problems, step by step

Two coins, or one coin twice, or two marbles out of a bag that is not refilled.

Practice Practice sheetNew questions
The question

What is the probability of getting an even number and an odd-numbered section? Give your answer in simplest form.

Someone rolled a number cube, then spun a spinner with 4 equal sections.
3/6
2/4
3/6 × 2/4 = 1/4
  1. Read it through once. Two things happen, and the question asks for BOTH of them to go your way. Work out each chance on its own first — the two never get added.
  2. The first one: 3 of the 6 are what you want, so 3/6.
  3. The second one: 2/4. Nothing the first did changes it — the second turn does not remember the first — so it is worked out exactly as if it happened alone.
  4. For BOTH, multiply: 3/6 × 2/4 = 1/4. Multiplying makes it smaller, which is right — both going your way is harder than either one on its own.

How it works.

  1. 01

    Read it through once. Two things happen, and the question asks for BOTH of them to go your way. Work out each chance on its own first — the two never get added.

  2. 02

    The first one: 3 of the 6 are what you want, so 3/6.

  3. 03

    The second one: 2/4. Nothing the first did changes it — the second turn does not remember the first — so it is worked out exactly as if it happened alone.

  4. 04

    For BOTH, multiply: 3/6 × 2/4 = 1/4. Multiplying makes it smaller, which is right — both going your way is harder than either one on its own.

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