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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 $17, $23, $29, and $35. What is the expected value E(X) of one spin?

    4 · $17 · $23 · $29 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?

    4 · $22 · $24 · $26 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $35, $45, and $55. What is the expected value E(X) of one spin?

    4 · $25 · $35 · $45 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    4 · $19 · $31 · $43 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?

    4 · $12 · $24 · $36 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $4, $16, $28, and $40. What is the expected value E(X) of one spin?

    4 · $4 · $16 · $28 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $12, $22, $32, and $42. What is the expected value E(X) of one spin?

    4 · $12 · $22 · $32 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $14, $18, $22, and $26. What is the expected value E(X) of one spin?

    4 · $14 · $18 · $22 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $8, $24, $40, and $56. What is the expected value E(X) of one spin?

    4 · $8 · $24 · $40 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?

    4 · $9 · $19 · $29 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    4 · $17 · $25 · $33 · Expected value & fair payo…
12 questions · Seed 104737 · 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 $17, $23, $29, and $35. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($17 + $23 + $29 + $35) ÷ 4 = $26.

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($22 + $24 + $26 + $28) ÷ 4 = $25.

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $35, $45, and $55. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($25 + $35 + $45 + $55) ÷ 4 = $40.

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($19 + $31 + $43 + $55) ÷ 4 = $37.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($12 + $24 + $36 + $48) ÷ 4 = $30.

  7. 7. A fair 4-sector spinner has equally likely prize values of $4, $16, $28, and $40. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($4 + $16 + $28 + $40) ÷ 4 = $22.

  8. 8. A fair 4-sector spinner has equally likely prize values of $12, $22, $32, and $42. What is the expected value E(X) of one spin?

    $27

    With 4 equally likely outcomes, E(X) = ($12 + $22 + $32 + $42) ÷ 4 = $27.

  9. 9. A fair 4-sector spinner has equally likely prize values of $14, $18, $22, and $26. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($14 + $18 + $22 + $26) ÷ 4 = $20.

  10. 10. A fair 4-sector spinner has equally likely prize values of $8, $24, $40, and $56. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($8 + $24 + $40 + $56) ÷ 4 = $32.

  11. 11. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($9 + $19 + $29 + $39) ÷ 4 = $24.

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($17 + $25 + $33 + $41) ÷ 4 = $29.

12 questions · Seed 104737 · 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 $17, $23, $29, and $35. What is the expected value E(X) of one spin?

    4 · $17 · $23 · $29 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?

    4 · $22 · $24 · $26 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $35, $45, and $55. What is the expected value E(X) of one spin?

    4 · $25 · $35 · $45 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    4 · $19 · $31 · $43 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?

    4 · $12 · $24 · $36 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $4, $16, $28, and $40. What is the expected value E(X) of one spin?

    4 · $4 · $16 · $28 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $12, $22, $32, and $42. What is the expected value E(X) of one spin?

    4 · $12 · $22 · $32 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $14, $18, $22, and $26. What is the expected value E(X) of one spin?

    4 · $14 · $18 · $22 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $8, $24, $40, and $56. What is the expected value E(X) of one spin?

    4 · $8 · $24 · $40 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?

    4 · $9 · $19 · $29 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    4 · $17 · $25 · $33 · Expected value & fair payo…
12 questions · Seed 104737 · 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 $17, $23, $29, and $35. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($17 + $23 + $29 + $35) ÷ 4 = $26.

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($22 + $24 + $26 + $28) ÷ 4 = $25.

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $35, $45, and $55. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($25 + $35 + $45 + $55) ÷ 4 = $40.

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($19 + $31 + $43 + $55) ÷ 4 = $37.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($12 + $24 + $36 + $48) ÷ 4 = $30.

  7. 7. A fair 4-sector spinner has equally likely prize values of $4, $16, $28, and $40. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($4 + $16 + $28 + $40) ÷ 4 = $22.

  8. 8. A fair 4-sector spinner has equally likely prize values of $12, $22, $32, and $42. What is the expected value E(X) of one spin?

    $27

    With 4 equally likely outcomes, E(X) = ($12 + $22 + $32 + $42) ÷ 4 = $27.

  9. 9. A fair 4-sector spinner has equally likely prize values of $14, $18, $22, and $26. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($14 + $18 + $22 + $26) ÷ 4 = $20.

  10. 10. A fair 4-sector spinner has equally likely prize values of $8, $24, $40, and $56. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($8 + $24 + $40 + $56) ÷ 4 = $32.

  11. 11. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($9 + $19 + $29 + $39) ÷ 4 = $24.

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($17 + $25 + $33 + $41) ÷ 4 = $29.

12 questions · Seed 104737 · Age guidance, not curriculum certification