The counting principle, and are these events independent?

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Luz's outfit is a top (one of 6 shirts or 4 sweaters) in one of 3 colors, plus a bag (one of 5 backpacks or 2 totes). How many different outfits are possible?

   210
2. 2.

   A 4-letter code uses the letters A to H, with no letter used twice and no vowels (A and E) allowed. Ren counts the codes. How many are possible?

   360
3. 3.

   Tala lines up 5 kids for a photo. Zee must stand first or last. In how many different orders can the kids line up?

   48
4. 4.

   A quiz team picks a captain and a different co-captain from n players, and there are 306 ways to do it. How many players are on Luz's team?

   18
5. 5.

   At Milo's school, events A and B are independent. P(A) = p, P(B) = p + 0.2, and P(A and B) = 0.15. What is P(A), as a fraction in simplest form?

   3/10
6. 6.

   At Noah's school, events A and B are independent. The chance A does not happen is 2/5, and P(A and B) = 3/10. What is P(B), in simplest form?

   1/2
7. 7.

   On Kira's two spinners with equal parts, events A and B are independent and P(A) = P(B). The chance of both is 4/25. What is P(A), in simplest form?

   2/5

8. Read this first

   Use this

   Two-way table of 120 students. Plays a sport and has a job: 12. Plays a sport, no job: 36. No sport, has a job: 18. No sport, no job: 54.

9. 8.

   Milo surveyed 120 students and made the two-way table. A is “plays a sport” and B is “has a job”. For a random student, are A and B independent?

   • Not independent: students with jobs have less time for sports
   • Not independent: 48 × 30 = 1,440, not 12
   • Independent: 48/120 × 30/120 = 12/120, the share with both
   • Not independent: 48/120 + 30/120 is not 12/120

10. Use this

    Two-way table of 100 students. Eats lunch at school and joins a club: 28. Eats lunch at school, no club: 42. Does not eat lunch at school, joins a club: 12. Does not eat lunch at school, no club: 18.

11. 9.

    Pia surveyed 100 students and made the two-way table. A is “eats lunch at school” and B is “joins a club”. For a random student, are A and B independent?

    • Independent: 70/100 × 40/100 = 28/100, the share with both
    • Not independent: 70 × 40 = 2,800, not 28
    • Not independent: 70/100 + 40/100 is not 28/100
    • Not independent: lunch might keep students at school for clubs

12. Use this

    Two-way table of 150 students. Owns a bike and a skateboard: 45. Owns a bike, no skateboard: 45. No bike, owns a skateboard: 15. No bike, no skateboard: 45.

13. 10.

    Kira surveyed 150 students and made the two-way table. A is “owns a bike” and B is “owns a skateboard”. For a random student, are A and B independent?

    • Independent: half of bike owners own a skateboard, so about half of the group does
    • Independent: bikes and skateboards are different things
    • Independent: 90/150 and 60/150 are close to each other
    • Not independent: 90/150 × 60/150 = 36/150, but 45/150 are in both