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)?

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

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

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

   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, so the events are mutually exclusive
   • 0.9, which is what you get by adding P(A) and P(B)
   • 0.2, and the events are independent since 0.5 × 0.4 = 0.2
5. 5.

   Survey of 60 students. Music and sport: 10. Music only: 20. Sport only: 14. Neither: 16. Milo reads a survey of 60 students about music and sport in the table. What is P(a student plays music or sport)?

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

   Noah knows P(A) = 1/2, P(B) = 1/3 and P(A or B) = 5/6. What is P(A and B)?

   • 1/3, since 5/6 − 1/2 = 1/3
   • 5/6, since that is P(A or B)
   • 0, since 1/2 + 1/3 − 5/6 = 0
   • 1/6, since 1/2 × 1/3 = 1/6
7. 7.

   Survey of 60 students. Music and sport: 10. Music only: 20. Sport only: 14. Neither: 16. Pia meets a student who plays music, using the survey table. What is the chance this student also plays sport?

   • 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
   • 10/24 = 5/12, out of the sport players
8. 8.

   40% of students ride the bus, and 50% of bus riders have a phone. Ren picks a student. What is P(bus rider with a phone)?

   • 0.4 × 0.5 = 0.2
   • 0.5 × 0.6 = 0.3, using the share who do not ride
   • 0.4 + 0.5 = 0.9
   • 0.5, the share of bus riders with a phone
9. 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
10. 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 × 0.5 = 0.15
    • 0.5, the chance of being late on a rainy day
    • 0.3 × 0.1 = 0.03, using the other-days rate
    • 0.3 + 0.5 = 0.8