The addition rule, and the general multiplication rule

Grade 11 Math Worksheet - Building Confidence

Circle the best answer.

1. 1.

   A club has 20 members: 10 play chess, 7 play robotics, 4 do both. Ari picks one member at random. What is P(chess or robotics)?

   • 7/20, because 7 of the 20 members play neither game
   • 10/20 + 7/20 = 17/20
   • 10/20 + 7/20 − 4/20 = 13/20
   • 10/20 × 7/20 = 7/40
2. 2.

   A bag holds 5 red, 3 blue and 4 green marbles. Bo draws one at random. What is P(red or blue)?

   • 4/12 = 1/3, since 4 marbles are green
   • 5/12 × 3/12 = 5/48
   • 5/12 + 3/12 − (5/12)(3/12) = 9/16, removing an overlap
   • 5/12 + 3/12 = 8/12 = 2/3, since no marble is both
3. 3.

   A hat holds 5 girls' names and 3 boys' names. Esme draws two names without putting any back. What is P(both boys)?

   • 3/8 × 2/8 = 3/32
   • 3/8 × 2/7 = 3/28
   • 3/8 × 3/8 = 9/64
   • 3/8 + 2/7 = 37/56
4. 4.

   A bag holds 4 red and 6 blue tiles. Jun draws two without replacing the first. What is P(red first, then blue)?

   • 4/10 × 3/9 = 2/15
   • 4/10 × 6/10 = 6/25
   • 4/10 × 6/9 = 4/15
   • 2 × (4/10 × 6/9) = 8/15, counting either order
5. 5.

   P(A) = 0.5, P(B) = 0.4 and P(A or B) = 0.7. Kira finds P(A and B). Which statement is right?

   • 0.3, the part of A outside B
   • 0.2, and the events are independent since 0.5 × 0.4 = 0.2
   • 0.2, so the events are mutually exclusive
   • 0.9, which is what you get by adding P(A) and P(B)
6. 6.

   Luz draws a tile numbered 1 to 12 at random. A is prime and B is odd. What is P(A or B)?

   • 5/12 + 6/12 − (5/12)(6/12) = 17/24, using a product for the overlap
   • 5/12 + 6/12 − 4/12 = 7/12, since 3, 5, 7 and 11 are in both
   • Just tile 3 is in both, so 5/12 + 6/12 − 1/12 = 5/6
   • 5/12 + 6/12 = 11/12

7. Read this first

   Use this

   Survey of 60 students. Music and sport: 10. Music only: 20. Sport only: 14. Neither: 16.

8. 7.

   Milo reads a survey of 60 students about music and sport in the table. What is P(a student plays music or sport)?

   • (20 + 14)/60 = 34/60 = 17/30
   • (30 + 24)/60 = 54/60 = 9/10
   • (10 + 20 + 14)/60 = 44/60 = 11/15
   • 10/60 = 1/6
9. 8.

   Pia meets a student who plays music, using the survey table. What is the chance this student also plays sport?

   • 10/24 = 5/12, out of the sport players
   • 10/60 = 1/6, out of the whole survey
   • 10/30 = 1/3, out of the music players
   • 24/60 = 2/5, the chance of sport overall
10. 9.

    P(A) = 0.3, P(B) = 0.2 and P(A and B) = 0.12. Tala finds P(B given A). Which is right?

    • 0.3 − 0.12 = 0.18
    • 0.12 ÷ 0.3 = 0.4
    • 0.12 ÷ 0.2 = 0.6
    • 0.3 × 0.12 = 0.036
11. 10.

    It rains on 30% of days. On rainy days Zee is late 50% of the time; on other days, 10%. What is P(rain and late)?

    • 0.3 × 0.1 = 0.03, using the other-days rate
    • 0.3 × 0.5 = 0.15
    • 0.5, the chance of being late on a rainy day
    • 0.3 + 0.5 = 0.8