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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 $20, $22, $24, and $26. What is the expected value E(X) of one spin?

    4 · $20 · $22 · $24 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $34, $46, and $58. What is the expected value E(X) of one spin?

    4 · $22 · $34 · $46 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?

    4 · $16 · $28 · $40 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $25, $27, and $29. What is the expected value E(X) of one spin?

    4 · $23 · $25 · $27 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $25, $41, $57, and $73. What is the expected value E(X) of one spin?

    4 · $25 · $41 · $57 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $10, $14, $18, and $22. What is the expected value E(X) of one spin?

    4 · $10 · $14 · $18 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    4 · $14 · $26 · $38 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $11, $21, $31, and $41. What is the expected value E(X) of one spin?

    4 · $11 · $21 · $31 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $19, $27, $35, and $43. What is the expected value E(X) of one spin?

    4 · $19 · $27 · $35 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $19, $21, $23, and $25. What is the expected value E(X) of one spin?

    4 · $19 · $21 · $23 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $29, $31, and $33. What is the expected value E(X) of one spin?

    4 · $27 · $29 · $31 · Expected value & fair payo…
12 questions · Seed 104735 · 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 $20, $22, $24, and $26. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($20 + $22 + $24 + $26) ÷ 4 = $23.

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $34, $46, and $58. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($22 + $34 + $46 + $58) ÷ 4 = $40.

  3. 3. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?

    $34

    With 4 equally likely outcomes, E(X) = ($16 + $28 + $40 + $52) ÷ 4 = $34.

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $25, $27, and $29. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($23 + $25 + $27 + $29) ÷ 4 = $26.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $25, $41, $57, and $73. What is the expected value E(X) of one spin?

    $49

    With 4 equally likely outcomes, E(X) = ($25 + $41 + $57 + $73) ÷ 4 = $49.

  7. 7. A fair 4-sector spinner has equally likely prize values of $10, $14, $18, and $22. What is the expected value E(X) of one spin?

    $16

    With 4 equally likely outcomes, E(X) = ($10 + $14 + $18 + $22) ÷ 4 = $16.

  8. 8. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($14 + $26 + $38 + $50) ÷ 4 = $32.

  9. 9. A fair 4-sector spinner has equally likely prize values of $11, $21, $31, and $41. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($11 + $21 + $31 + $41) ÷ 4 = $26.

  10. 10. A fair 4-sector spinner has equally likely prize values of $19, $27, $35, and $43. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($19 + $27 + $35 + $43) ÷ 4 = $31.

  11. 11. A fair 4-sector spinner has equally likely prize values of $19, $21, $23, and $25. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($19 + $21 + $23 + $25) ÷ 4 = $22.

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $29, $31, and $33. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($27 + $29 + $31 + $33) ÷ 4 = $30.

12 questions · Seed 104735 · 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 $20, $22, $24, and $26. What is the expected value E(X) of one spin?

    4 · $20 · $22 · $24 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $34, $46, and $58. What is the expected value E(X) of one spin?

    4 · $22 · $34 · $46 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?

    4 · $16 · $28 · $40 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $25, $27, and $29. What is the expected value E(X) of one spin?

    4 · $23 · $25 · $27 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $25, $41, $57, and $73. What is the expected value E(X) of one spin?

    4 · $25 · $41 · $57 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $10, $14, $18, and $22. What is the expected value E(X) of one spin?

    4 · $10 · $14 · $18 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    4 · $14 · $26 · $38 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $11, $21, $31, and $41. What is the expected value E(X) of one spin?

    4 · $11 · $21 · $31 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $19, $27, $35, and $43. What is the expected value E(X) of one spin?

    4 · $19 · $27 · $35 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $19, $21, $23, and $25. What is the expected value E(X) of one spin?

    4 · $19 · $21 · $23 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $29, $31, and $33. What is the expected value E(X) of one spin?

    4 · $27 · $29 · $31 · Expected value & fair payo…
12 questions · Seed 104735 · 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 $20, $22, $24, and $26. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($20 + $22 + $24 + $26) ÷ 4 = $23.

  2. 2. A fair 4-sector spinner has equally likely prize values of $22, $34, $46, and $58. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($22 + $34 + $46 + $58) ÷ 4 = $40.

  3. 3. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?

    $34

    With 4 equally likely outcomes, E(X) = ($16 + $28 + $40 + $52) ÷ 4 = $34.

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $25, $27, and $29. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($23 + $25 + $27 + $29) ÷ 4 = $26.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $25, $41, $57, and $73. What is the expected value E(X) of one spin?

    $49

    With 4 equally likely outcomes, E(X) = ($25 + $41 + $57 + $73) ÷ 4 = $49.

  7. 7. A fair 4-sector spinner has equally likely prize values of $10, $14, $18, and $22. What is the expected value E(X) of one spin?

    $16

    With 4 equally likely outcomes, E(X) = ($10 + $14 + $18 + $22) ÷ 4 = $16.

  8. 8. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($14 + $26 + $38 + $50) ÷ 4 = $32.

  9. 9. A fair 4-sector spinner has equally likely prize values of $11, $21, $31, and $41. What is the expected value E(X) of one spin?

    $26

    With 4 equally likely outcomes, E(X) = ($11 + $21 + $31 + $41) ÷ 4 = $26.

  10. 10. A fair 4-sector spinner has equally likely prize values of $19, $27, $35, and $43. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($19 + $27 + $35 + $43) ÷ 4 = $31.

  11. 11. A fair 4-sector spinner has equally likely prize values of $19, $21, $23, and $25. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($19 + $21 + $23 + $25) ÷ 4 = $22.

  12. 12. A fair 4-sector spinner has equally likely prize values of $27, $29, $31, and $33. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($27 + $29 + $31 + $33) ÷ 4 = $30.

12 questions · Seed 104735 · Age guidance, not curriculum certification