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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 $27, $31, $35, and $39. What is the expected value E(X) of one spin?

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

  2. 2. A fair 4-sector spinner has equally likely prize values of $27, $37, $47, and $57. What is the expected value E(X) of one spin?

    4 · $27 · $37 · $47 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $29, $33, and $37. What is the expected value E(X) of one spin?

    4 · $25 · $29 · $33 · Expected value & fair payo…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $28, $32, $36, and $40. What is the expected value E(X) of one spin?

    4 · $28 · $32 · $36 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $6, $18, $30, and $42. What is the expected value E(X) of one spin?

    4 · $6 · $18 · $30 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $21, $31, $41, and $51. What is the expected value E(X) of one spin?

    4 · $21 · $31 · $41 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $28, $44, and $60. What is the expected value E(X) of one spin?

    4 · $12 · $28 · $44 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $27, $41, $55, and $69. What is the expected value E(X) of one spin?

    4 · $27 · $41 · $55 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?

    4 · $22 · $32 · $42 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?

    4 · $30 · $34 · $38 · Expected value & fair payo…
12 questions · Seed 104745 · 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 $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.

  2. 2. A fair 4-sector spinner has equally likely prize values of $27, $37, $47, and $57. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($27 + $37 + $47 + $57) ÷ 4 = $42.

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $29, $33, and $37. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($25 + $29 + $33 + $37) ÷ 4 = $31.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $28, $32, $36, and $40. What is the expected value E(X) of one spin?

    $34

    With 4 equally likely outcomes, E(X) = ($28 + $32 + $36 + $40) ÷ 4 = $34.

  6. 6. A fair 4-sector spinner has equally likely prize values of $6, $18, $30, and $42. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($6 + $18 + $30 + $42) ÷ 4 = $24.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $21, $31, $41, and $51. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($21 + $31 + $41 + $51) ÷ 4 = $36.

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $28, $44, and $60. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($12 + $28 + $44 + $60) ÷ 4 = $36.

  10. 10. A fair 4-sector spinner has equally likely prize values of $27, $41, $55, and $69. What is the expected value E(X) of one spin?

    $48

    With 4 equally likely outcomes, E(X) = ($27 + $41 + $55 + $69) ÷ 4 = $48.

  11. 11. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($22 + $32 + $42 + $52) ÷ 4 = $37.

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($30 + $34 + $38 + $42) ÷ 4 = $36.

12 questions · Seed 104745 · 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 $27, $31, $35, and $39. What is the expected value E(X) of one spin?

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

  2. 2. A fair 4-sector spinner has equally likely prize values of $27, $37, $47, and $57. What is the expected value E(X) of one spin?

    4 · $27 · $37 · $47 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $29, $33, and $37. What is the expected value E(X) of one spin?

    4 · $25 · $29 · $33 · Expected value & fair payo…

  4. 4. 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…

  5. 5. A fair 4-sector spinner has equally likely prize values of $28, $32, $36, and $40. What is the expected value E(X) of one spin?

    4 · $28 · $32 · $36 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $6, $18, $30, and $42. What is the expected value E(X) of one spin?

    4 · $6 · $18 · $30 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $21, $31, $41, and $51. What is the expected value E(X) of one spin?

    4 · $21 · $31 · $41 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $28, $44, and $60. What is the expected value E(X) of one spin?

    4 · $12 · $28 · $44 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $27, $41, $55, and $69. What is the expected value E(X) of one spin?

    4 · $27 · $41 · $55 · Expected value & fair payo…

  11. 11. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?

    4 · $22 · $32 · $42 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?

    4 · $30 · $34 · $38 · Expected value & fair payo…
12 questions · Seed 104745 · 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 $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.

  2. 2. A fair 4-sector spinner has equally likely prize values of $27, $37, $47, and $57. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($27 + $37 + $47 + $57) ÷ 4 = $42.

  3. 3. A fair 4-sector spinner has equally likely prize values of $25, $29, $33, and $37. What is the expected value E(X) of one spin?

    $31

    With 4 equally likely outcomes, E(X) = ($25 + $29 + $33 + $37) ÷ 4 = $31.

  4. 4. 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.

  5. 5. A fair 4-sector spinner has equally likely prize values of $28, $32, $36, and $40. What is the expected value E(X) of one spin?

    $34

    With 4 equally likely outcomes, E(X) = ($28 + $32 + $36 + $40) ÷ 4 = $34.

  6. 6. A fair 4-sector spinner has equally likely prize values of $6, $18, $30, and $42. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($6 + $18 + $30 + $42) ÷ 4 = $24.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $21, $31, $41, and $51. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($21 + $31 + $41 + $51) ÷ 4 = $36.

  9. 9. A fair 4-sector spinner has equally likely prize values of $12, $28, $44, and $60. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($12 + $28 + $44 + $60) ÷ 4 = $36.

  10. 10. A fair 4-sector spinner has equally likely prize values of $27, $41, $55, and $69. What is the expected value E(X) of one spin?

    $48

    With 4 equally likely outcomes, E(X) = ($27 + $41 + $55 + $69) ÷ 4 = $48.

  11. 11. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($22 + $32 + $42 + $52) ÷ 4 = $37.

  12. 12. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($30 + $34 + $38 + $42) ÷ 4 = $36.

12 questions · Seed 104745 · Age guidance, not curriculum certification