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

2. 1.

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

   17
3. 2.

   Zee's lock has n dials, and each dial shows a digit from 0 to 9. Which expression gives the number of different codes?

   • 10^n
   • 10n
   • n^10
   • 10 + n
4. 3.

   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?

   • n³
   • n + (n − 1) + (n − 2)
   • 3n
   • n(n − 1)(n − 2)
5. 4.

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

   • s + 3 + 4
   • 4 × s × 3
   • 4(s + 3)
   • 4s + 3
6. 5.

   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
   • 5n
   • 5 + n
   • 5^n
7. 6.

   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)/2
   • n(n − 1)
   • 2n
8. 7.

   In Luz's class, 40% bike to school, 30% have a dog, and 12% do both. A is “bikes” and B is “has a dog”. Are A and B independent?

   • Not independent: 12% is smaller than both 40% and 30%
   • Not independent: 0.4 + 0.3 = 0.7, not 0.12
   • Not independent: dog walkers get exercise, so biking changes
   • Independent: 0.4 × 0.3 = 0.12, which is P(A and B)
9. 8.

   On 60% of days in Noah's town it is sunny, on 50% it is warm, and on 40% it is both. A is “sunny” and B is “warm”. Are A and B independent?

   • Independent: 0.4 is close enough to 0.3
   • Independent: 0.6 and 0.5 are close to each other
   • Independent: sunny and warm are different things, so one cannot change the other
   • Not independent: 0.6 × 0.5 = 0.3, but P(A and B) = 0.4
10. 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?

    • Independent: 0.3 × 0.5 = 0.15, which is P(A and B)
    • Not independent: 0.7 × 0.5 = 0.35, not 0.15
    • Not independent: both events come from the same spin of the spinner
    • Not independent: 0.3 + 0.5 is not 0.15
11. 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?

    • Independent: 0.4 and 0.5 are close to each other
    • 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: 0.6 × 0.5 = 0.3 is close to 0.25