The counting principle, and are these events independent?

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Use this

   Tree diagram. First branches: beach and park. Beach: 3 activities, and each activity splits into 2 snacks. Park: 4 activities, and each activity splits into 2 snacks.

2. 1.

   Bo drew a weekend tree (with one very sleepy dog) that starts with two places. How many different weekends does the tree show?

   14

3. Use this

   Tree diagram. First branches: fruit and crackers. Fruit: 4 kinds, and each kind splits into 2 dips. Crackers: 3 kinds, and each kind splits into 3 spreads.

4. 2.

   Luz's snack tree starts with fruit or crackers. How many different snacks does the tree show?

   17
5. 3.

   Tala's pizza tree (it grew a giant branch) starts with thin or thick crust. How many different pizzas does the tree show?

   19

6. Use this

   Soup: 3 kinds, each with 2 breads. Salad: 4 kinds, each with 2 dressings. Wrap: 2 kinds, each with 3 sides.

7. 4.

   Ren's lunch tree starts with soup, salad or wrap. How many different lunches does the tree show?

   20
8. 5.

   A class gives first, second and third place to 3 of n posters. A poster can win only once. Ari wants the number of ways. Which expression counts them?

   • n(n − 1)(n − 2)
   • 3n
   • n + (n − 1) + (n − 2)
   • n³
9. 6.

   Bo's lunch is one of s sandwiches or one of 3 salads, plus one of 4 drinks. Which expression counts the different lunches?

   • 4s + 3
   • s + 3 + 4
   • 4(s + 3)
   • 4 × s × 3
10. 7.

    Each of n students picks one of 5 clubs, and many students can pick the same club. Esme wants the number of ways. Which expression fits?

    • n^5
    • 5^n
    • 5 + n
    • 5n
11. 8.

    Kira picks a first book and a different second book to read from n books on a shelf. Which expression counts the ways to pick?

    • n²
    • n(n − 1)
    • 2n
    • n(n − 1)/2
12. 9.

    On Milo's spinner (equal parts), A is “red” and B is “even”. The chance of not red is 0.7, P(B) = 0.5 and P(A and B) = 0.15. Are A and B independent?

    • Not independent: both events come from the same spin of the spinner
    • Not independent: 0.7 × 0.5 = 0.35, not 0.15
    • Not independent: 0.3 + 0.5 is not 0.15
    • Independent: 0.3 × 0.5 = 0.15, which is P(A and B)
13. 10.

    On Kira's route, A is “bus late” and B is “rain”. The chance of on time is 0.6, P(B) = 0.5 and P(A and B) = 0.25. Are A and B independent?

    • Not independent: 0.4 × 0.5 = 0.2, but P(A and B) = 0.25
    • Independent: rain and a late bus look unrelated to each other, so they pass
    • Independent: 0.4 and 0.5 are close to each other
    • Independent: 0.6 × 0.5 = 0.3 is close to 0.25