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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 $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    4 · $12 · $16 · $20 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $12, $18, $24, and $30. What is the expected value E(X) of one spin?

    4 · $12 · $18 · $24 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $8, $18, $28, and $38. What is the expected value E(X) of one spin?

    4 · $8 · $18 · $28 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $10, $18, $26, and $34. What is the expected value E(X) of one spin?

    4 · $10 · $18 · $26 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $32, $48, and $64. What is the expected value E(X) of one spin?

    4 · $16 · $32 · $48 · Expected value & fair payo…

  6. 6. 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…

  7. 7. A fair 4-sector spinner has equally likely prize values of $29, $39, $49, and $59. What is the expected value E(X) of one spin?

    4 · $29 · $39 · $49 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $16, $18, $20, and $22. What is the expected value E(X) of one spin?

    4 · $16 · $18 · $20 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $16, $22, $28, and $34. What is the expected value E(X) of one spin?

    4 · $16 · $22 · $28 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?

    4 · $24 · $38 · $52 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $11, $13, $15, and $17. What is the expected value E(X) of one spin?

    4 · $11 · $13 · $15 · Expected value & fair payo…
12 questions · Seed 104729 · 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 $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    $18

    With 4 equally likely outcomes, E(X) = ($12 + $16 + $20 + $24) ÷ 4 = $18.

  2. 2. A fair 4-sector spinner has equally likely prize values of $12, $18, $24, and $30. What is the expected value E(X) of one spin?

    $21

    With 4 equally likely outcomes, E(X) = ($12 + $18 + $24 + $30) ÷ 4 = $21.

  3. 3. A fair 4-sector spinner has equally likely prize values of $8, $18, $28, and $38. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($8 + $18 + $28 + $38) ÷ 4 = $23.

  4. 4. A fair 4-sector spinner has equally likely prize values of $10, $18, $26, and $34. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($10 + $18 + $26 + $34) ÷ 4 = $22.

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $32, $48, and $64. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($16 + $32 + $48 + $64) ÷ 4 = $40.

  6. 6. 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.

  7. 7. A fair 4-sector spinner has equally likely prize values of $29, $39, $49, and $59. What is the expected value E(X) of one spin?

    $44

    With 4 equally likely outcomes, E(X) = ($29 + $39 + $49 + $59) ÷ 4 = $44.

  8. 8. A fair 4-sector spinner has equally likely prize values of $16, $18, $20, and $22. What is the expected value E(X) of one spin?

    $19

    With 4 equally likely outcomes, E(X) = ($16 + $18 + $20 + $22) ÷ 4 = $19.

  9. 9. A fair 4-sector spinner has equally likely prize values of $16, $22, $28, and $34. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($16 + $22 + $28 + $34) ÷ 4 = $25.

  10. 10. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($24 + $38 + $52 + $66) ÷ 4 = $45.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $11, $13, $15, and $17. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($11 + $13 + $15 + $17) ÷ 4 = $14.

12 questions · Seed 104729 · 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 $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    4 · $12 · $16 · $20 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $12, $18, $24, and $30. What is the expected value E(X) of one spin?

    4 · $12 · $18 · $24 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $8, $18, $28, and $38. What is the expected value E(X) of one spin?

    4 · $8 · $18 · $28 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $10, $18, $26, and $34. What is the expected value E(X) of one spin?

    4 · $10 · $18 · $26 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $32, $48, and $64. What is the expected value E(X) of one spin?

    4 · $16 · $32 · $48 · Expected value & fair payo…

  6. 6. 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…

  7. 7. A fair 4-sector spinner has equally likely prize values of $29, $39, $49, and $59. What is the expected value E(X) of one spin?

    4 · $29 · $39 · $49 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $16, $18, $20, and $22. What is the expected value E(X) of one spin?

    4 · $16 · $18 · $20 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $16, $22, $28, and $34. What is the expected value E(X) of one spin?

    4 · $16 · $22 · $28 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?

    4 · $24 · $38 · $52 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $11, $13, $15, and $17. What is the expected value E(X) of one spin?

    4 · $11 · $13 · $15 · Expected value & fair payo…
12 questions · Seed 104729 · 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 $12, $16, $20, and $24. What is the expected value E(X) of one spin?

    $18

    With 4 equally likely outcomes, E(X) = ($12 + $16 + $20 + $24) ÷ 4 = $18.

  2. 2. A fair 4-sector spinner has equally likely prize values of $12, $18, $24, and $30. What is the expected value E(X) of one spin?

    $21

    With 4 equally likely outcomes, E(X) = ($12 + $18 + $24 + $30) ÷ 4 = $21.

  3. 3. A fair 4-sector spinner has equally likely prize values of $8, $18, $28, and $38. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($8 + $18 + $28 + $38) ÷ 4 = $23.

  4. 4. A fair 4-sector spinner has equally likely prize values of $10, $18, $26, and $34. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($10 + $18 + $26 + $34) ÷ 4 = $22.

  5. 5. A fair 4-sector spinner has equally likely prize values of $16, $32, $48, and $64. What is the expected value E(X) of one spin?

    $40

    With 4 equally likely outcomes, E(X) = ($16 + $32 + $48 + $64) ÷ 4 = $40.

  6. 6. 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.

  7. 7. A fair 4-sector spinner has equally likely prize values of $29, $39, $49, and $59. What is the expected value E(X) of one spin?

    $44

    With 4 equally likely outcomes, E(X) = ($29 + $39 + $49 + $59) ÷ 4 = $44.

  8. 8. A fair 4-sector spinner has equally likely prize values of $16, $18, $20, and $22. What is the expected value E(X) of one spin?

    $19

    With 4 equally likely outcomes, E(X) = ($16 + $18 + $20 + $22) ÷ 4 = $19.

  9. 9. A fair 4-sector spinner has equally likely prize values of $16, $22, $28, and $34. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($16 + $22 + $28 + $34) ÷ 4 = $25.

  10. 10. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?

    $45

    With 4 equally likely outcomes, E(X) = ($24 + $38 + $52 + $66) ÷ 4 = $45.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $11, $13, $15, and $17. What is the expected value E(X) of one spin?

    $14

    With 4 equally likely outcomes, E(X) = ($11 + $13 + $15 + $17) ÷ 4 = $14.

12 questions · Seed 104729 · Age guidance, not curriculum certification