Grade 8 · Math · Unit 11 of 18
Chance with Many Events
Venn diagrams, trees and dependent events
What your child practises
Using Venn diagrams and tree diagrams, finding the probability of two or more independent events, comparing drawing with and without replacement, and comparing experimental with theoretical probability.
Ontario Curriculum expectation: D2.1, D2.2 · probability using Venn and tree diagrams, and independent and dependent events
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
A tree diagram shows a choice of 3 shirts, then 4 pants, then 2 hats. How many different outfits are there?
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24
Hint: Multiply the number of branches at each step.
Question 2
In a class of 40, 15 students are in art club and 12 are in music club. 6 students are in both clubs. How many students are in only art?
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9
Hint: Draw a Venn diagram. Start with the overlap, then fill in the rest of each circle. Parts add to the total.
Question 3
A spinner has 6 equal sections numbered 1 to 6. It is spun, and a coin is flipped. What is P(a 1 and tails)? Type a fraction.
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1/12
Hint: For independent events, multiply the probabilities of each event.
Question 4
A bag has 4 red and 6 blue marbles. Two marbles are drawn one after the other without putting the first back. What is P(both red)? Type a fraction in lowest terms.
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2/15
Hint: P(first red) = 4/10. With one red gone, P(second red) = 3/9. Multiply them.
Question 5
Are these events independent or dependent? Choosing a name from a hat, keeping it out, then choosing a second name.
- independent
- dependent
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dependent
Hint: Events are dependent when the first outcome changes the probability of the second. Putting an item back makes events independent.
Question 6
A spinner is spun 60 times and lands on green 13 times. What is the experimental probability of green? Type a fraction in lowest terms.
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13/60
Hint: Experimental probability = number of times it happened ÷ number of trials.