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.

   Pia's 3-digit code uses digits 0 to 9, with no digit used twice. The first digit is not 0 and the last digit is odd. How many codes are possible?

   320
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.

   A race gives gold, silver and bronze to three different runners out of n runners. There are 210 ways to give the medals. How many runners are in Esme's race?

   7
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: 48/120 + 30/120 is not 12/120
   • Not independent: 48 × 30 = 1,440, not 12
   • Independent: 48/120 × 30/120 = 12/120, the share with both

10. Use this

    Two-way table of 200 students. Rides the bus and eats breakfast at school: 24. Rides the bus, no breakfast: 56. Does not ride, eats breakfast: 26. Does not ride, no breakfast: 94.

11. 9.

    Noah surveyed 200 students and made the two-way table. A is “rides the bus” and B is “eats breakfast at school”. For a random student, are A and B independent?

    • Independent: 24 is close to 20, so the table passes
    • Independent: 80/200 and 50/200 are close to each other
    • Independent: riding the bus has nothing to do with breakfast
    • Not independent: 80/200 × 50/200 = 20/200, but 24/200 are in both

12. 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.

13. 10.

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