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Probability word problems, step by step

Probability starts with one draw from a bag.

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The question

What is the probability that it is NOT green? Write your answer in simplest form.

A jar has 8 green beads and 4 blue beads. One bead is picked at random.
12 altogether
not green → 4
4 out of 12
1/3
  1. Read it through once. A probability is not a sum to work out — it is a COUNT over a COUNT: how many outcomes you want, over how many there are altogether.
  2. Count the whole set first, because it is the bottom number and it never changes: 12 altogether.
  3. Now the top. The question asks for "not green", so it is not the ones you can see — it is everything ELSE. Take them off the total: that leaves 4. Giving the count you were shown is the usual mistake here.
  4. Write the top over the bottom: 4 over 12, then simplify — 1/3. The answer is a fraction, not a division to finish.

How it works.

  1. 01

    Read it through once. A probability is not a sum to work out — it is a COUNT over a COUNT: how many outcomes you want, over how many there are altogether.

  2. 02

    Count the whole set first, because it is the bottom number and it never changes: 12 altogether.

  3. 03

    Now the top. The question asks for "not green", so it is not the ones you can see — it is everything ELSE. Take them off the total: that leaves 4. Giving the count you were shown is the usual mistake here.

  4. 04

    Write the top over the bottom: 4 over 12, then simplify — 1/3. The answer is a fraction, not a division to finish.

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