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. Use this

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

4. 2.

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

   20
5. 3.

   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
   • n^10
   • 10 + n
   • 10n
6. 4.

   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)
   • n + (n − 1) + (n − 2)
   • n³
   • 3n
7. 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?

   • 5^n
   • 5n
   • 5 + n
   • n^5
8. 6.

   Jun's snack is one of f fruits or one of 4 chips, plus one of 3 dips. Which expression counts the different snacks?

   • 3f + 4
   • 3 × f × 4
   • f + 4 + 3
   • 3(f + 4)
9. 7.

   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?

   • 2n
   • n²
   • n(n − 1)
   • n(n − 1)/2
10. 8.

    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?

    • Independent: 0.4 × 0.3 = 0.12, which is P(A and B)
    • Not independent: 12% is smaller than both 40% and 30%
    • Not independent: dog walkers get exercise, so biking changes
    • Not independent: 0.4 + 0.3 = 0.7, not 0.12
11. 9.

    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
    • Not independent: 0.6 × 0.5 = 0.3, but P(A and B) = 0.4
    • Independent: sunny and warm are different things, so one cannot change the other
    • Independent: 0.6 and 0.5 are close to each other
12. 10.

    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: 0.3 + 0.5 is not 0.15
    • 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