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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 $26, $40, $54, and $68. What is the expected value E(X) of one spin?

    4 · $26 · $40 · $54 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $7, $15, $23, and $31. What is the expected value E(X) of one spin?

    4 · $7 · $15 · $23 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?

    4 · $14 · $24 · $34 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $15, $25, $35, and $45. What is the expected value E(X) of one spin?

    4 · $15 · $25 · $35 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $17, $21, $25, and $29. What is the expected value E(X) of one spin?

    4 · $17 · $21 · $25 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $11, $17, $23, and $29. What is the expected value E(X) of one spin?

    4 · $11 · $17 · $23 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $30, $40, $50, and $60. What is the expected value E(X) of one spin?

    4 · $30 · $40 · $50 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $24, $26, $28, and $30. What is the expected value E(X) of one spin?

    4 · $24 · $26 · $28 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    4 · $12 · $16 · $20 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    4 · $30 · $36 · $42 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $33, $39, and $45. What is the expected value E(X) of one spin?

    4 · $27 · $33 · $39 · Expected value & fair payo…
12 questions · Seed 104738 · 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 $26, $40, $54, and $68. What is the expected value E(X) of one spin?

    $47

    With 4 equally likely outcomes, E(X) = ($26 + $40 + $54 + $68) ÷ 4 = $47.

  2. 2. A fair 4-sector spinner has equally likely prize values of $7, $15, $23, and $31. What is the expected value E(X) of one spin?

    $19

    With 4 equally likely outcomes, E(X) = ($7 + $15 + $23 + $31) ÷ 4 = $19.

  3. 3. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($14 + $24 + $34 + $44) ÷ 4 = $29.

  4. 4. A fair 4-sector spinner has equally likely prize values of $15, $25, $35, and $45. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($15 + $25 + $35 + $45) ÷ 4 = $30.

  5. 5. A fair 4-sector spinner has equally likely prize values of $17, $21, $25, and $29. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($17 + $21 + $25 + $29) ÷ 4 = $23.

  6. 6. A fair 4-sector spinner has equally likely prize values of $11, $17, $23, and $29. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($11 + $17 + $23 + $29) ÷ 4 = $20.

  7. 7. A fair 4-sector spinner has equally likely prize values of $30, $40, $50, and $60. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($30 + $40 + $50 + $60) ÷ 4 = $45.

  8. 8. A fair 4-sector spinner has equally likely prize values of $24, $26, $28, and $30. What is the expected value E(X) of one spin?

    $27

    With 4 equally likely outcomes, E(X) = ($24 + $26 + $28 + $30) ÷ 4 = $27.

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    $18

    With 4 equally likely outcomes, E(X) = ($12 + $16 + $20 + $24) ÷ 4 = $18.

  10. 10. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($30 + $36 + $42 + $48) ÷ 4 = $39.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $33, $39, and $45. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($27 + $33 + $39 + $45) ÷ 4 = $36.

12 questions · Seed 104738 · 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 $26, $40, $54, and $68. What is the expected value E(X) of one spin?

    4 · $26 · $40 · $54 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $7, $15, $23, and $31. What is the expected value E(X) of one spin?

    4 · $7 · $15 · $23 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?

    4 · $14 · $24 · $34 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $15, $25, $35, and $45. What is the expected value E(X) of one spin?

    4 · $15 · $25 · $35 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $17, $21, $25, and $29. What is the expected value E(X) of one spin?

    4 · $17 · $21 · $25 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $11, $17, $23, and $29. What is the expected value E(X) of one spin?

    4 · $11 · $17 · $23 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $30, $40, $50, and $60. What is the expected value E(X) of one spin?

    4 · $30 · $40 · $50 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $24, $26, $28, and $30. What is the expected value E(X) of one spin?

    4 · $24 · $26 · $28 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    4 · $12 · $16 · $20 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    4 · $30 · $36 · $42 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $33, $39, and $45. What is the expected value E(X) of one spin?

    4 · $27 · $33 · $39 · Expected value & fair payo…
12 questions · Seed 104738 · 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 $26, $40, $54, and $68. What is the expected value E(X) of one spin?

    $47

    With 4 equally likely outcomes, E(X) = ($26 + $40 + $54 + $68) ÷ 4 = $47.

  2. 2. A fair 4-sector spinner has equally likely prize values of $7, $15, $23, and $31. What is the expected value E(X) of one spin?

    $19

    With 4 equally likely outcomes, E(X) = ($7 + $15 + $23 + $31) ÷ 4 = $19.

  3. 3. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($14 + $24 + $34 + $44) ÷ 4 = $29.

  4. 4. A fair 4-sector spinner has equally likely prize values of $15, $25, $35, and $45. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($15 + $25 + $35 + $45) ÷ 4 = $30.

  5. 5. A fair 4-sector spinner has equally likely prize values of $17, $21, $25, and $29. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($17 + $21 + $25 + $29) ÷ 4 = $23.

  6. 6. A fair 4-sector spinner has equally likely prize values of $11, $17, $23, and $29. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($11 + $17 + $23 + $29) ÷ 4 = $20.

  7. 7. A fair 4-sector spinner has equally likely prize values of $30, $40, $50, and $60. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($30 + $40 + $50 + $60) ÷ 4 = $45.

  8. 8. A fair 4-sector spinner has equally likely prize values of $24, $26, $28, and $30. What is the expected value E(X) of one spin?

    $27

    With 4 equally likely outcomes, E(X) = ($24 + $26 + $28 + $30) ÷ 4 = $27.

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    $18

    With 4 equally likely outcomes, E(X) = ($12 + $16 + $20 + $24) ÷ 4 = $18.

  10. 10. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($30 + $36 + $42 + $48) ÷ 4 = $39.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $33, $39, and $45. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($27 + $33 + $39 + $45) ÷ 4 = $36.

12 questions · Seed 104738 · Age guidance, not curriculum certification