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Grade 8 · Math · Unit 11 of 11

Independent Events

Multiply probabilities of events that don't affect each other

What your child practises

Finding the chance that two separate events both happen, such as a coin toss and a die roll, by multiplying their probabilities.

Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Statistics and Probability · the probability of two independent events, and verifying with a tree diagram

How we explain it

Children can open this short lesson before they practise.

  1. Independent events do not change each other's chances.
  2. Multiply their probabilities to find the chance of both.
  3. A tree diagram can check your answer.

Example: A coin lands heads and a die lands on 6. What is the probability of both? Heads: 1/2. Six: 1/6. 1/2 × 1/6 = 1/12. Answer: 1/12

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Spinner A has 5 equal sections numbered 1 to 5. Spinner B has 7 equal sections numbered 1 to 7. Both are spun. What is P(1 on A and 1 on B)? Type a fraction.

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  2. Question 2

    A die is rolled twice. What is P(a 5 or a 6 both times)? Type a fraction in lowest terms.

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  3. Question 3

    A coin is tossed 3 times. A tree diagram shows every possible outcome. How many outcomes are there?

    • 7
    • 8
    • 10
    • 6

  4. Question 4

    Events A and B are independent. P(A) = 0.3 and P(B) = 0.4. What is P(A and B)?

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  5. Question 5

    A coin is tossed and a die is rolled. What is P(heads and a 6)? Type a fraction in lowest terms.

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  6. Question 6

    Which pair of events is independent?

    • tossing a coin and rolling a die
    • choosing two students from a team, one after the other, with no repeats
    • it rains today and the school cancels outdoor recess
    • drawing two cards from a deck, one after the other, without putting the first back

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