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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 $28, $34, $40, and $46. What is the expected value E(X) of one spin?

    4 · $28 · $34 · $40 · Expected value & fair payo…

  2. 2. 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…

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $38, $46, and $54. What is the expected value E(X) of one spin?

    4 · $30 · $38 · $46 · Expected value & fair payo…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?

    4 · $7 · $9 · $11 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?

    4 · $7 · $19 · $31 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $8, $12, $16, and $20. What is the expected value E(X) of one spin?

    4 · $8 · $12 · $16 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $29, $41, and $53. What is the expected value E(X) of one spin?

    4 · $17 · $29 · $41 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $20, $30, $40, and $50. What is the expected value E(X) of one spin?

    4 · $20 · $30 · $40 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $20, $24, and $28. What is the expected value E(X) of one spin?

    4 · $16 · $20 · $24 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $25, $41, and $57. What is the expected value E(X) of one spin?

    4 · $9 · $25 · $41 · Expected value & fair payo…
12 questions · Seed 104730 · 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 $28, $34, $40, and $46. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($28 + $34 + $40 + $46) ÷ 4 = $37.

  2. 2. 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.

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $38, $46, and $54. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($30 + $38 + $46 + $54) ÷ 4 = $42.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?

    $10

    With 4 equally likely outcomes, E(X) = ($7 + $9 + $11 + $13) ÷ 4 = $10.

  6. 6. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($7 + $19 + $31 + $43) ÷ 4 = $25.

  7. 7. A fair 4-sector spinner has equally likely prize values of $8, $12, $16, and $20. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($8 + $12 + $16 + $20) ÷ 4 = $14.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $29, $41, and $53. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($17 + $29 + $41 + $53) ÷ 4 = $35.

  9. 9. A fair 4-sector spinner has equally likely prize values of $20, $30, $40, and $50. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($20 + $30 + $40 + $50) ÷ 4 = $35.

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $20, $24, and $28. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($16 + $20 + $24 + $28) ÷ 4 = $22.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $25, $41, and $57. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($9 + $25 + $41 + $57) ÷ 4 = $33.

12 questions · Seed 104730 · 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 $28, $34, $40, and $46. What is the expected value E(X) of one spin?

    4 · $28 · $34 · $40 · Expected value & fair payo…

  2. 2. 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…

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $38, $46, and $54. What is the expected value E(X) of one spin?

    4 · $30 · $38 · $46 · Expected value & fair payo…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?

    4 · $7 · $9 · $11 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?

    4 · $7 · $19 · $31 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $8, $12, $16, and $20. What is the expected value E(X) of one spin?

    4 · $8 · $12 · $16 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $29, $41, and $53. What is the expected value E(X) of one spin?

    4 · $17 · $29 · $41 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $20, $30, $40, and $50. What is the expected value E(X) of one spin?

    4 · $20 · $30 · $40 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $20, $24, and $28. What is the expected value E(X) of one spin?

    4 · $16 · $20 · $24 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $25, $41, and $57. What is the expected value E(X) of one spin?

    4 · $9 · $25 · $41 · Expected value & fair payo…
12 questions · Seed 104730 · 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 $28, $34, $40, and $46. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($28 + $34 + $40 + $46) ÷ 4 = $37.

  2. 2. 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.

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $38, $46, and $54. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($30 + $38 + $46 + $54) ÷ 4 = $42.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?

    $10

    With 4 equally likely outcomes, E(X) = ($7 + $9 + $11 + $13) ÷ 4 = $10.

  6. 6. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($7 + $19 + $31 + $43) ÷ 4 = $25.

  7. 7. A fair 4-sector spinner has equally likely prize values of $8, $12, $16, and $20. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($8 + $12 + $16 + $20) ÷ 4 = $14.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $29, $41, and $53. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($17 + $29 + $41 + $53) ÷ 4 = $35.

  9. 9. A fair 4-sector spinner has equally likely prize values of $20, $30, $40, and $50. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($20 + $30 + $40 + $50) ÷ 4 = $35.

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $20, $24, and $28. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($16 + $20 + $24 + $28) ÷ 4 = $22.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $25, $41, and $57. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($9 + $25 + $41 + $57) ÷ 4 = $33.

12 questions · Seed 104730 · Age guidance, not curriculum certification