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Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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The addition rule, and the general multiplication rule

Grade 11 Math Worksheet - Building Confidence

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

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

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

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

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

  5. 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
    • Just tile 3 is in both, so 5/12 + 6/12 − 1/12 = 5/6
    • 5/12 + 6/12 − 4/12 = 7/12, since 3, 5, 7 and 11 are in both
    • 5/12 + 6/12 = 11/12

  6. 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)?

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

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

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

  8. 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?

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

  9. 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)?

    • 0.5, the share of bus riders with a phone
    • 0.4 + 0.5 = 0.9
    • 0.4 × 0.5 = 0.2
    • 0.5 × 0.6 = 0.3, using the share who do not ride

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