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10th grade Conditional probability, from outcomes or from a two-way table, and what it says about independence worksheet

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Conditional probability, from outcomes or from a two-way table, and what it says about independence

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

  1. For a random student in Luz's club, P(sport) = 3/5 and P(sport and instrument) = 1/4. Given sport, what is the chance of instrument, in simplest form?

  2. For a random student in Milo's club, P(pet) = 2/3 and P(pet and garden) = 1/6. Given pet, what is the chance of garden, in simplest form?

  3. Read this first

    Two-way table of students, counts only (no totals)

    Grade 9Grade 10
    Swims1317
    Does not swim228

  4. Pia asked students about the swim unit. A student who is in grade 10 is picked at random. What is the chance the student swims, in simplest form?

  5. Ren counted lunch choices at the school cafe. A student who has late lunch is picked at random. What is the chance the student picks soup, in simplest form?

  6. Tala asked students how they get around. A student who lives far from school is picked at random. What is the chance the student owns no scooter, in simplest form?

  7. Two-way table of plants, counts only

    FloweredDid not flower
    Sunny window1421
    Shady shelf8empty

  8. Ari's table of plants has one empty cell. What number in the empty cell makes flowering independent of the spot?

  9. Two-way table of students, counts only

    Passed the swim testNot yet
    Morning class124
    Afternoon class15empty

  10. Bo's table of students has one empty cell. What number in the empty cell makes passing the swim test independent of the class time?

  11. For a random student at Esme's school, P(walks to school) = 1/3, P(has a pet) = 3/5 and P(both) = 1/5. Are the two events independent?

    • No: 1/5 is less than both chances
    • Yes: 1/3 × 3/5 = 1/5
    • No: P(A) = 1/3 is not the same as P(B) = 3/5
    • No: 1/3 + 3/5 = 14/15, not 1/5

  12. For a random student at Jun's school, P(plays chess) = 2/5, P(plays a sport) = 1/4 and P(both) = 1/5. Are the two events independent?

    • No: 2/5 + 1/4 = 13/20, not 1/5
    • No: P(A) = 2/5 is not the same as P(B) = 1/4
    • No: 2/5 × 1/4 = 1/10, not 1/5
    • Yes: "plays chess" and "plays a sport" are about different things

  13. For a random student at Kira's school, P(eats lunch at school) = 3/5, P(is in band) = 1/4 and P(both) = 3/20. Are the two events independent?

    • No: P(A) = 3/5 is not the same as P(B) = 1/4
    • Yes: 3/5 × 1/4 = 3/20
    • No: 3/5 + 1/4 = 17/20, not 3/20
    • No: 3/20 is less than both chances
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10th grade Conditional probability, from outcomes or from a two-way table, and what it says about independence worksheet – printable
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About this worksheet

Conditional probability from outcome lists and two-way tables. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find P(A given B) by keeping only the outcomes where B happens.
  • I can read joint, marginal and conditional chances from a two-way table.
  • I can decide from the numbers whether knowing one fact changes a chance.

Standard: S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6

Words to know

outcome list: Every result that can happen, written one per row.

given: We already know this happened, so only those rows count.

joint chance: The chance two things happen together, out of everyone.

marginal chance: The chance of one thing, from a row or column total.

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

Common mistakes

Divided by everyone instead of by the group named after "given".

Found the chance the other way round, dividing by the wrong group. Read the sentence aloud and point to the group after "given".

Divided by a row total when the question was about everyone.

What to say

Ask: which group are we told about? Count only that group.

Ask: is any group given? If not, use the grand total.

Questions parents ask

What is the most common mistake with conditional probability, from outcomes or from a two-way table, and what it says about independence?

Divided by everyone instead of by the group named after "given".

How can I help my child with conditional probability, from outcomes or from a two-way table, and what it says about independence?

Ask: which group are we told about? Count only that group.

Are these 10th 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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