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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 $18, $34, $50, and $66. What is the expected value E(X) of one spin?

    4 · $18 · $34 · $50 · Expected value & fair payo…

  3. 3. 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…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $29, $43, $57, and $71. What is the expected value E(X) of one spin?

    4 · $29 · $43 · $57 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    4 · $21 · $27 · $33 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?

    4 · $22 · $28 · $34 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?

    4 · $27 · $31 · $35 · Expected value & fair payo…

  9. 9. 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…

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $21, $27, and $33. What is the expected value E(X) of one spin?

    4 · $15 · $21 · $27 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $5, $15, $25, and $35. What is the expected value E(X) of one spin?

    4 · $5 · $15 · $25 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $3, $5, $7, and $9. What is the expected value E(X) of one spin?

    4 · $3 · $5 · $7 · Expected value & fair payo…
12 questions · Seed 104742 · 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 $18, $34, $50, and $66. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($18 + $34 + $50 + $66) ÷ 4 = $42.

  3. 3. 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.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $29, $43, $57, and $71. What is the expected value E(X) of one spin?

    $50

    With 4 equally likely outcomes, E(X) = ($29 + $43 + $57 + $71) ÷ 4 = $50.

  6. 6. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($21 + $27 + $33 + $39) ÷ 4 = $30.

  7. 7. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($22 + $28 + $34 + $40) ÷ 4 = $31.

  8. 8. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($27 + $31 + $35 + $39) ÷ 4 = $33.

  9. 9. 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.

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $21, $27, and $33. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($15 + $21 + $27 + $33) ÷ 4 = $24.

  11. 11. A fair 4-sector spinner has equally likely prize values of $5, $15, $25, and $35. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($5 + $15 + $25 + $35) ÷ 4 = $20.

  12. 12. A fair 4-sector spinner has equally likely prize values of $3, $5, $7, and $9. What is the expected value E(X) of one spin?

    $6

    With 4 equally likely outcomes, E(X) = ($3 + $5 + $7 + $9) ÷ 4 = $6.

12 questions · Seed 104742 · 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 $18, $34, $50, and $66. What is the expected value E(X) of one spin?

    4 · $18 · $34 · $50 · Expected value & fair payo…

  3. 3. 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…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $29, $43, $57, and $71. What is the expected value E(X) of one spin?

    4 · $29 · $43 · $57 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    4 · $21 · $27 · $33 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?

    4 · $22 · $28 · $34 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?

    4 · $27 · $31 · $35 · Expected value & fair payo…

  9. 9. 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…

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $21, $27, and $33. What is the expected value E(X) of one spin?

    4 · $15 · $21 · $27 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $5, $15, $25, and $35. What is the expected value E(X) of one spin?

    4 · $5 · $15 · $25 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $3, $5, $7, and $9. What is the expected value E(X) of one spin?

    4 · $3 · $5 · $7 · Expected value & fair payo…
12 questions · Seed 104742 · 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 $18, $34, $50, and $66. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($18 + $34 + $50 + $66) ÷ 4 = $42.

  3. 3. 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.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $29, $43, $57, and $71. What is the expected value E(X) of one spin?

    $50

    With 4 equally likely outcomes, E(X) = ($29 + $43 + $57 + $71) ÷ 4 = $50.

  6. 6. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($21 + $27 + $33 + $39) ÷ 4 = $30.

  7. 7. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($22 + $28 + $34 + $40) ÷ 4 = $31.

  8. 8. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($27 + $31 + $35 + $39) ÷ 4 = $33.

  9. 9. 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.

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $21, $27, and $33. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($15 + $21 + $27 + $33) ÷ 4 = $24.

  11. 11. A fair 4-sector spinner has equally likely prize values of $5, $15, $25, and $35. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($5 + $15 + $25 + $35) ÷ 4 = $20.

  12. 12. A fair 4-sector spinner has equally likely prize values of $3, $5, $7, and $9. What is the expected value E(X) of one spin?

    $6

    With 4 equally likely outcomes, E(X) = ($3 + $5 + $7 + $9) ÷ 4 = $6.

12 questions · Seed 104742 · Age guidance, not curriculum certification