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ReasoningAges 16-18

Expected value & fair payouts

Calculate the expected monetary payout per trial from outcome probabilities and payoffs. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Expected value & fair payouts

Take your time. Show your thinking.

  1. 1. A fair 4-sector spinner has equally likely prize values of $12, $20, $28, and $36. What is the expected value E(X) of one spin?

    4 · $12 · $20 · $28 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    4 · $23 · $35 · $47 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    4 · $13 · $19 · $25 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $8, $20, $32, and $44. What is the expected value E(X) of one spin?

    4 · $8 · $20 · $32 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $18, $28, $38, and $48. What is the expected value E(X) of one spin?

    4 · $18 · $28 · $38 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $27, $39, $51, and $63. What is the expected value E(X) of one spin?

    4 · $27 · $39 · $51 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $24, $30, $36, and $42. What is the expected value E(X) of one spin?

    4 · $24 · $30 · $36 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    4 · $26 · $28 · $30 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?

    4 · $29 · $31 · $33 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    4 · $17 · $19 · $21 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    4 · $11 · $25 · $39 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    4 · $30 · $32 · $34 · Expected value & fair payo…
12 questions · Seed 104743 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Expected value & fair payouts

Answers and reasoning. Review before teaching.

  1. 1. A fair 4-sector spinner has equally likely prize values of $12, $20, $28, and $36. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($12 + $20 + $28 + $36) ÷ 4 = $24.

  2. 2. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($23 + $35 + $47 + $59) ÷ 4 = $41.

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($13 + $19 + $25 + $31) ÷ 4 = $22.

  4. 4. A fair 4-sector spinner has equally likely prize values of $8, $20, $32, and $44. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($8 + $20 + $32 + $44) ÷ 4 = $26.

  5. 5. A fair 4-sector spinner has equally likely prize values of $18, $28, $38, and $48. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($18 + $28 + $38 + $48) ÷ 4 = $33.

  6. 6. A fair 4-sector spinner has equally likely prize values of $27, $39, $51, and $63. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($27 + $39 + $51 + $63) ÷ 4 = $45.

  7. 7. A fair 4-sector spinner has equally likely prize values of $24, $30, $36, and $42. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($24 + $30 + $36 + $42) ÷ 4 = $33.

  8. 8. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($26 + $28 + $30 + $32) ÷ 4 = $29.

  9. 9. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($29 + $31 + $33 + $35) ÷ 4 = $32.

  10. 10. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.

  11. 11. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($11 + $25 + $39 + $53) ÷ 4 = $32.

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.

12 questions · Seed 104743 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Expected value & fair payouts

Take your time. Show your thinking.

  1. 1. A fair 4-sector spinner has equally likely prize values of $12, $20, $28, and $36. What is the expected value E(X) of one spin?

    4 · $12 · $20 · $28 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    4 · $23 · $35 · $47 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    4 · $13 · $19 · $25 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $8, $20, $32, and $44. What is the expected value E(X) of one spin?

    4 · $8 · $20 · $32 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $18, $28, $38, and $48. What is the expected value E(X) of one spin?

    4 · $18 · $28 · $38 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $27, $39, $51, and $63. What is the expected value E(X) of one spin?

    4 · $27 · $39 · $51 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $24, $30, $36, and $42. What is the expected value E(X) of one spin?

    4 · $24 · $30 · $36 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    4 · $26 · $28 · $30 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?

    4 · $29 · $31 · $33 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    4 · $17 · $19 · $21 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    4 · $11 · $25 · $39 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    4 · $30 · $32 · $34 · Expected value & fair payo…
12 questions · Seed 104743 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Expected value & fair payouts

Answers and reasoning. Review before teaching.

  1. 1. A fair 4-sector spinner has equally likely prize values of $12, $20, $28, and $36. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($12 + $20 + $28 + $36) ÷ 4 = $24.

  2. 2. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($23 + $35 + $47 + $59) ÷ 4 = $41.

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($13 + $19 + $25 + $31) ÷ 4 = $22.

  4. 4. A fair 4-sector spinner has equally likely prize values of $8, $20, $32, and $44. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($8 + $20 + $32 + $44) ÷ 4 = $26.

  5. 5. A fair 4-sector spinner has equally likely prize values of $18, $28, $38, and $48. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($18 + $28 + $38 + $48) ÷ 4 = $33.

  6. 6. A fair 4-sector spinner has equally likely prize values of $27, $39, $51, and $63. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($27 + $39 + $51 + $63) ÷ 4 = $45.

  7. 7. A fair 4-sector spinner has equally likely prize values of $24, $30, $36, and $42. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($24 + $30 + $36 + $42) ÷ 4 = $33.

  8. 8. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($26 + $28 + $30 + $32) ÷ 4 = $29.

  9. 9. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($29 + $31 + $33 + $35) ÷ 4 = $32.

  10. 10. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.

  11. 11. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($11 + $25 + $39 + $53) ÷ 4 = $32.

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.

12 questions · Seed 104743 · Age guidance, not curriculum certification