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Grade 11 · Math · Algebra 2

11th grade The addition rule, and the general multiplication rule worksheet

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The addition rule, and the general multiplication rule

Grade 11 Math Worksheet

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Circle the best answer.

  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: 0.625 and 0.5 are close enough to be equal
    • Independent: P(sport) + P(music) = 0.9, which is under 1
    • 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. 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 and B) = 0.8 − 0.5 = 0.3 differs from P(B) = 0.6
    • Independent: P(A and B) = 0.5 + 0.6 − 0.8 = 0.3, and 0.5 × 0.6 = 0.3
    • Not independent: P(A or B) = 0.8 differs from 0.5 × 0.6 = 0.3
    • Not independent: A and B overlap by 0.3, so they share outcomes

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

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

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

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

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

  6. 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)³ = 27/125
    • 6/10 × 5/10 × 4/10 = 3/25
    • 6/10 × 5/9 × 4/8 = 1/6

  7. P(A) = 0.5 and P(B) = 0.3. Pia asks how small and how large P(A or B) can be. Which range is right?

    • From 0.3 up to 0.8: the smaller chance is the least it can be
    • From 0.5 up to 1: the two events could cover everything
    • Exactly 0.8, since A and B are different events
    • From 0.5 up to 0.8: B inside A gives 0.5, no overlap gives 0.8

  8. 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 − 0.15 = 0.45
    • 1 − (0.4 + 0.35) = 0.25
    • 0.4 + 0.35 − 0.15 = 0.6, the chance of A or B
    • 1 − (0.4 + 0.35 − 0.15) = 0.4

  9. 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 − 0.3 × 0.25 = 0.475
    • 0.3 + 0.25 − 0.3 × 0.4 = 0.43
    • 0.3 + 0.25 − 0.4 = 0.15

  10. Machine A makes 60% of parts, 2% defective. Machine B makes 40%, 5% defective. Zee picks a part at random. What is P(defective)?

    • 0.02 + 0.05 = 0.07
    • 0.6 × 0.05 + 0.4 × 0.02 = 0.038
    • 0.6 × 0.02 + 0.4 × 0.05 = 0.032
    • 0.6 × 0.02 = 0.012, from machine A
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11th grade The addition rule, and the general multiplication rule worksheet – printable
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About this worksheet

The addition rule and the general multiplication rule. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find P(A or B) and P(A and B) with the addition and general multiplication rules, and say when nothing is subtracted.
  • I can test independence from a table or from three chances, and read and reverse a conditional chance.
  • I can follow every path of a no-put-back draw, find a total over two sources and reverse it, and judge a probability argument.

Standard: S-CP.B.7, S-CP.B.8 (+)

Words to know

mutually exclusive: Two events that cannot both happen: no outcome is in both.

independent: Knowing one event happened does not change the chance of the other.

P(B given A): The chance of B once A has happened.

addition rule: P(A or B) = P(A) + P(B) − P(A and B).

multiplication rule: P(A and B) = P(A) × P(B given A).

Common mistakes

Your child added two chances and did not subtract what was counted twice.

Your child used the wrong rule: multiplied for 'or', added for 'and', or divided where multiplying was needed.

Your child kept the same total for every draw, as if each item were put back.

What to say

Ask: which outcomes sit in both groups?

Ask: does the question ask for one event or both?

Ask: how many are left after the first draw?

Questions parents ask

What is the most common mistake with the addition rule, and the general multiplication rule?

Your child added two chances and did not subtract what was counted twice.

How can I help my child with the addition rule, and the general multiplication rule?

Ask: which outcomes sit in both groups?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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