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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 $25, $33, $41, and $49. What is the expected value E(X) of one spin?

    4 · $25 · $33 · $41 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $2, $10, $18, and $26. What is the expected value E(X) of one spin?

    4 · $2 · $10 · $18 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $3, $11, $19, and $27. What is the expected value E(X) of one spin?

    4 · $3 · $11 · $19 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?

    4 · $28 · $40 · $52 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $24, $32, and $40. What is the expected value E(X) of one spin?

    4 · $16 · $24 · $32 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $14, $30, $46, and $62. What is the expected value E(X) of one spin?

    4 · $14 · $30 · $46 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $28, $44, $60, and $76. What is the expected value E(X) of one spin?

    4 · $28 · $44 · $60 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $23, $39, $55, and $71. What is the expected value E(X) of one spin?

    4 · $23 · $39 · $55 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $9, $11, $13, and $15. What is the expected value E(X) of one spin?

    4 · $9 · $11 · $13 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $27, $39, and $51. What is the expected value E(X) of one spin?

    4 · $15 · $27 · $39 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    4 · $30 · $32 · $34 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $13, $15, $17, and $19. What is the expected value E(X) of one spin?

    4 · $13 · $15 · $17 · Expected value & fair payo…
12 questions · Seed 104731 · 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 $25, $33, $41, and $49. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($25 + $33 + $41 + $49) ÷ 4 = $37.

  2. 2. A fair 4-sector spinner has equally likely prize values of $2, $10, $18, and $26. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($2 + $10 + $18 + $26) ÷ 4 = $14.

  3. 3. A fair 4-sector spinner has equally likely prize values of $3, $11, $19, and $27. What is the expected value E(X) of one spin?

    $15

    With 4 equally likely outcomes, E(X) = ($3 + $11 + $19 + $27) ÷ 4 = $15.

  4. 4. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?

    $46

    With 4 equally likely outcomes, E(X) = ($28 + $40 + $52 + $64) ÷ 4 = $46.

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $24, $32, and $40. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($16 + $24 + $32 + $40) ÷ 4 = $28.

  6. 6. A fair 4-sector spinner has equally likely prize values of $14, $30, $46, and $62. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($14 + $30 + $46 + $62) ÷ 4 = $38.

  7. 7. A fair 4-sector spinner has equally likely prize values of $28, $44, $60, and $76. What is the expected value E(X) of one spin?

    $52

    With 4 equally likely outcomes, E(X) = ($28 + $44 + $60 + $76) ÷ 4 = $52.

  8. 8. A fair 4-sector spinner has equally likely prize values of $23, $39, $55, and $71. What is the expected value E(X) of one spin?

    $47

    With 4 equally likely outcomes, E(X) = ($23 + $39 + $55 + $71) ÷ 4 = $47.

  9. 9. A fair 4-sector spinner has equally likely prize values of $9, $11, $13, and $15. What is the expected value E(X) of one spin?

    $12

    With 4 equally likely outcomes, E(X) = ($9 + $11 + $13 + $15) ÷ 4 = $12.

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $27, $39, and $51. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($15 + $27 + $39 + $51) ÷ 4 = $33.

  11. 11. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.

  12. 12. A fair 4-sector spinner has equally likely prize values of $13, $15, $17, and $19. What is the expected value E(X) of one spin?

    $16

    With 4 equally likely outcomes, E(X) = ($13 + $15 + $17 + $19) ÷ 4 = $16.

12 questions · Seed 104731 · 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 $25, $33, $41, and $49. What is the expected value E(X) of one spin?

    4 · $25 · $33 · $41 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $2, $10, $18, and $26. What is the expected value E(X) of one spin?

    4 · $2 · $10 · $18 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $3, $11, $19, and $27. What is the expected value E(X) of one spin?

    4 · $3 · $11 · $19 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?

    4 · $28 · $40 · $52 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $24, $32, and $40. What is the expected value E(X) of one spin?

    4 · $16 · $24 · $32 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $14, $30, $46, and $62. What is the expected value E(X) of one spin?

    4 · $14 · $30 · $46 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $28, $44, $60, and $76. What is the expected value E(X) of one spin?

    4 · $28 · $44 · $60 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $23, $39, $55, and $71. What is the expected value E(X) of one spin?

    4 · $23 · $39 · $55 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $9, $11, $13, and $15. What is the expected value E(X) of one spin?

    4 · $9 · $11 · $13 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $27, $39, and $51. What is the expected value E(X) of one spin?

    4 · $15 · $27 · $39 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    4 · $30 · $32 · $34 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $13, $15, $17, and $19. What is the expected value E(X) of one spin?

    4 · $13 · $15 · $17 · Expected value & fair payo…
12 questions · Seed 104731 · 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 $25, $33, $41, and $49. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($25 + $33 + $41 + $49) ÷ 4 = $37.

  2. 2. A fair 4-sector spinner has equally likely prize values of $2, $10, $18, and $26. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($2 + $10 + $18 + $26) ÷ 4 = $14.

  3. 3. A fair 4-sector spinner has equally likely prize values of $3, $11, $19, and $27. What is the expected value E(X) of one spin?

    $15

    With 4 equally likely outcomes, E(X) = ($3 + $11 + $19 + $27) ÷ 4 = $15.

  4. 4. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?

    $46

    With 4 equally likely outcomes, E(X) = ($28 + $40 + $52 + $64) ÷ 4 = $46.

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $24, $32, and $40. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($16 + $24 + $32 + $40) ÷ 4 = $28.

  6. 6. A fair 4-sector spinner has equally likely prize values of $14, $30, $46, and $62. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($14 + $30 + $46 + $62) ÷ 4 = $38.

  7. 7. A fair 4-sector spinner has equally likely prize values of $28, $44, $60, and $76. What is the expected value E(X) of one spin?

    $52

    With 4 equally likely outcomes, E(X) = ($28 + $44 + $60 + $76) ÷ 4 = $52.

  8. 8. A fair 4-sector spinner has equally likely prize values of $23, $39, $55, and $71. What is the expected value E(X) of one spin?

    $47

    With 4 equally likely outcomes, E(X) = ($23 + $39 + $55 + $71) ÷ 4 = $47.

  9. 9. A fair 4-sector spinner has equally likely prize values of $9, $11, $13, and $15. What is the expected value E(X) of one spin?

    $12

    With 4 equally likely outcomes, E(X) = ($9 + $11 + $13 + $15) ÷ 4 = $12.

  10. 10. A fair 4-sector spinner has equally likely prize values of $15, $27, $39, and $51. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($15 + $27 + $39 + $51) ÷ 4 = $33.

  11. 11. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?

    $33

    With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.

  12. 12. A fair 4-sector spinner has equally likely prize values of $13, $15, $17, and $19. What is the expected value E(X) of one spin?

    $16

    With 4 equally likely outcomes, E(X) = ($13 + $15 + $17 + $19) ÷ 4 = $16.

12 questions · Seed 104731 · Age guidance, not curriculum certification