Grade 8 · Math · Unit 13 of 13
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.
Alberta Curriculum learning outcome: SP2 · the probability of two independent events, and verifying with a tree diagram
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
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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1/35
Hint: P(1 on A) = 1/5 and P(1 on B) = 1/7. Multiply: 1/5 × 1/7 = 1/35.
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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1/9
Hint: P(a 5 or a 6) = 1/3 each time. Multiply: 1/3 × 1/3 = 1/9.
Question 3
A coin is tossed 3 times. A tree diagram shows every possible outcome. How many outcomes are there?
- 7
- 8
- 10
- 6
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8
Hint: Each toss has 2 outcomes, so there are 2 × 2 × 2 = 8 outcomes.
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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0.12
Hint: Multiply: 0.3 × 0.4 = 0.12.
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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1/12
Hint: P(heads) = 1/2 and P(a 6) = 1/6. For independent events, multiply: 1/2 × 1/6 = 1/12.
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
Show answer
tossing a coin and rolling a die
Hint: Events are independent when the first one does not change the chances of the second.