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Lesson 8 of 16

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6 min

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A set has 12 cards: 4 red, 4 blue, 4 green. Each colour has the numbers 1, 2, 3, 4. You pick one card without looking. What is P(not red)?

Count all: 12 cards. Not 3 colours!
Step 1 of 4
  1. Count all: 12 cards. Not 3 colours!
  2. Count wanted for red: 4 cards. P(red) = 4/12 = 1/3.
  3. Use the rule: P(not red) = 1 − 1/3 = 2/3.
  4. Check: blue + green = 8 cards. 8/12 = 2/3. It matches.

Not red is 8 cards of 12. The chance is 2/3.

The five steps

  1. Count all the outcomes.
  2. Check they are equally likely. Same-size cards, well shuffled: yes.
  3. Count the wanted outcomes.
  4. Use the rule the question needs: ÷, "not", or "or".
  5. Check another way.

One more

Same cards. What is P(a 1 or a 4)?

  1. Cards with 1: 3. Cards with 4: 3.
  2. No card has both, because each card shows one number. So add: 3 + 3 = 6.
  3. P = 6/12 = 1/2.

Watch out!

Counting 2 colours out of 3 also gives 2/3. That number is right here, but the method is wrong. Try 5 red, 4 blue and 3 green cards. Colours still say 2/3. The cards say 7/12. Count cards, not colours.

Now try it. Tap the cards that fit each question.

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