11F: Q30 Probability (Tree Diagrams & Contingency Tables)

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1. There are 240 boys in Grade 11. The following information on participation in school sport was collected: 122 boys play rugby. (R) 58 boys play hockey. (H) 96 boys play cricket. (C) 16 boys take part in all three sports. 22 boys take part in rugby and hockey. 26 boys take part in cricket and hockey. 26 boys do not participate in any of the sports. Let the number of learners playing rugby and cricket be 𝑥 Calculate the value of 𝑥.

• A. 12
• B. 13
• C. 14

2. You have a pack of cards with 52 cards in total. You draw one card from the pack and then put it back. You then draw a second card. What is the probability that they were both hearts?

• A. 1/4
• B. 1/8
• C. 1/16

3. A coin is flipped and a dice is rolled. Determine the probability of getting tails and an even number.

• A. 1/6
• B. 1/4
• C. 1/3

4. A bag contains 6 blue, 5 red and 9 white marbles. A marble is drawn and replaced, and another marble is then drawn. Draw a tree diagram to represent this information and use it to determine the probability that both marbles are white.

• A. 0.1
• B. 0.2
• C. 0.3

5. A bag contains 8 white balls, 6 black balls and 7 green balls. A ball is drawn at random and not replaced. A second ball is drawn. Determine the probability that both balls are green.

• A. 1/10
• B. 2/10
• C. 3/10

6. What is the probability of a randomly chosen person from this Year 7 class being a boy and their favourite sports being athletics?

• A. 0.13
• B. 0.17
• C. 0.27

7. What is the probability of a randomly chosen person from this Year 7 class being a boy?

• A. 0.41
• B. 0.48
• C. 0.54