The addition rule, and the general multiplication rule

Grade 11 Math Worksheet

Circle the best answer.

1. 1.

   Survey of 200 students. Sport and music: 50. Sport only: 50. Music only: 30. Neither: 70. Ari tests whether playing sport and playing music are independent in a survey of 200 students. Which conclusion fits?

   • Independent: P(sport) + P(music) = 0.9, which is under 1
   • Independent: 0.625 and 0.5 are close enough to be equal
   • Independent: 50 students do both, so the two groups overlap
   • Not independent: P(sport | music) = 50/80 = 0.625, but P(sport) = 0.5
2. 2.

   P(A) = 0.5, P(B) = 0.6 and P(A or B) = 0.8. Bo tests whether A and B are independent. Which conclusion fits?

   • Not independent: P(A or B) = 0.8 differs from 0.5 × 0.6 = 0.3
   • Not independent: P(A and B) = 0.8 − 0.5 = 0.3 differs from P(B) = 0.6
   • Not independent: A and B overlap by 0.3, so they share outcomes
   • Independent: P(A and B) = 0.5 + 0.6 − 0.8 = 0.3, and 0.5 × 0.6 = 0.3
3. 3.

   P(A) = 0.5, P(B) = 0.6 and P(A and B) = 0.18. Esme finds P(A given B). What does it show?

   • 0.18 ÷ 0.6 = 0.3, close to P(A) = 0.5, so they are independent
   • 0.18 × 0.6 = 0.108, so B makes A very unlikely
   • 0.18 ÷ 0.5 = 0.36, below P(B) = 0.6, so A lowers the chance of B
   • 0.18 ÷ 0.6 = 0.3, below P(A) = 0.5, so B lowers the chance of A
4. 4.

   P(A) = 0.4, P(B | A) = 0.6 and P(B) = 0.5. Jun finds P(A given B). Which is right?

   • 0.4 × 0.6 ÷ 0.5 = 0.48
   • 0.6, the same as P(B | A)
   • 0.4 × 0.6 = 0.24, the chance of A and B
   • 0.4 ÷ 0.5 = 0.8, dividing the two single chances
5. 5.

   A jar has 5 red and 4 green marbles. Kira draws two without putting any back. What is P(two different colors)?

   • 5/9 × 4/8 = 5/18, red then green
   • 5/9 × 4/9 + 4/9 × 5/9 = 40/81
   • 5/9 × 4/8 + 4/9 × 5/8 = 5/9
   • 5/9 × 4/8 + 4/9 × 3/8 = 4/9, both the same color
6. 6.

   The same jar holds 5 red and 4 green marbles. Luz draws two without putting any back. What is P(at least one red)?

   • 4/9 × 3/8 = 1/6, no red marbles
   • 5/9 × 4/8 = 5/18, two reds
   • 1 − 4/9 × 4/9 = 65/81
   • 1 − 4/9 × 3/8 = 5/6
7. 7.

   A bag has 3 red and 5 green marbles. Milo draws two without replacement. What is P(the second marble is red)?

   • 3/7, because the first marble was green
   • 3/8 × 2/7 + 5/8 × 3/7 = 3/8
   • 3/8 × 2/7 = 3/28, red then red
   • 2/7, because the first marble was red
8. 8.

   A drawer holds 6 black and 4 white socks. Noah pulls three in the dark, keeping each. What is P(all three black)?

   • 3 × (6/10 × 5/9 × 4/8) = 1/2, counting three orders
   • 6/10 × 5/9 × 4/8 = 1/6
   • 6/10 × 5/10 × 4/10 = 3/25
   • (6/10)³ = 27/125
9. 9.

   P(A) = 0.4, P(B) = 0.35 and P(A and B) = 0.15. Ren finds P(neither A nor B). Which is right?

   • 1 − (0.4 + 0.35 − 0.15) = 0.4
   • 1 − 0.4 − 0.15 = 0.45
   • 0.4 + 0.35 − 0.15 = 0.6, the chance of A or B
   • 1 − (0.4 + 0.35) = 0.25
10. 10.

    30% of students take art and 25% take music. Of art students, 40% also take music. Tala picks a student. What is P(art or music)?

    • 0.3 + 0.25 = 0.55
    • 0.3 + 0.25 − 0.4 = 0.15
    • 0.3 + 0.25 − 0.3 × 0.25 = 0.475
    • 0.3 + 0.25 − 0.3 × 0.4 = 0.43