Conditional Probability from Tables and Venn Diagrams · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Given that changes everything

Mathematics · Probability · ages 15-16
Name ______________________   Date ____________

  1. 80 boys, 20 play tennis. What is P(tennis given boy)?

    Answer: ______________

  2. 200 students: 120 girls, 30 of them play tennis. What is P(tennis given girl)?

    • 0.15
    • 0.6
    • 0.3
    • 0.25

  3. P(tennis given girl) uses which pupils as its denominator?

    • Only the girls
    • All pupils
    • Only tennis players

  4. Venn: A-only 12, both 8, B-only 20. To find P(A given B), you circle B first.

    Circle one:   True   False

  5. 50 tennis players, 30 are girls. What is P(girl given tennis player)?

    Answer: ______________

  6. Same Venn: A-only 12, both 8, B-only 20. What is P(B given A)?

    • 2/7
    • 8/28
    • 0.4

  7. Venn: A only 12, both 8, B only 20. What is P(A given B)?

    • 8/40
    • 8/20
    • 2/7
    • 1/2

  8. Maya says the denominator of P(A given B) counts only the B cases. Is Maya right?

    Circle one:   True   False

  9. A test spots 99% of cases, yet most people who test positive are healthy. What best explains this?

    • The test is broken
    • The condition is rare, so false alarms dominate
    • 99% is a small number

  10. Venn: A only 10, both 15, B only 10. What is P(A given B)?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Given that changes everything W1-mt_Vx88ugViYP-s1

  1. 0.25 · 20 over 80 = 0.25.
  2. 0.25 · 30 over row total 120 = 0.25. The 0.15 option wrongly uses all 200.
  3. Only the girls · GIVEN names the group: only the girls count underneath.
  4. True · Circle the given set first, then count inside it.
  5. 0.6 · 30 over 50 = 0.6.
  6. 0.4 · Circle A holds 20, so 8 over 20 = 0.4.
  7. 2/7 · 8 over B total 28, simplified to 2 over 7. The 8 over 40 option uses everybody.
  8. True · Given B restricts the world to B.
  9. The condition is rare, so false alarms dominate · Given a positive result, the denominator is full of healthy people when the condition is rare.
  10. 0.6 · 15 over 25 = 0.6.
Worksheet · LightMySky