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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 $8, $22, $36, and $50. What is the expected value E(X) of one spin?

    4 · $8 · $22 · $36 · Expected value & fair payo…

  2. 2. 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…

  3. 3. 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…

  4. 4. 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…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $5, $17, $29, and $41. What is the expected value E(X) of one spin?

    4 · $5 · $17 · $29 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $26, $36, $46, and $56. What is the expected value E(X) of one spin?

    4 · $26 · $36 · $46 · Expected value & fair payo…

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

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

  9. 9. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?

    4 · $10 · $22 · $34 · Expected value & fair payo…

  10. 10. 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…

  11. 11. A fair 4-sector spinner has equally likely prize values of $21, $35, $49, and $63. What is the expected value E(X) of one spin?

    4 · $21 · $35 · $49 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $19, $35, $51, and $67. What is the expected value E(X) of one spin?

    4 · $19 · $35 · $51 · Expected value & fair payo…
12 questions · Seed 104732 · 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 $8, $22, $36, and $50. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($8 + $22 + $36 + $50) ÷ 4 = $29.

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $5, $17, $29, and $41. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($5 + $17 + $29 + $41) ÷ 4 = $23.

  7. 7. A fair 4-sector spinner has equally likely prize values of $26, $36, $46, and $56. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($26 + $36 + $46 + $56) ÷ 4 = $41.

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

    $10

    With 4 equally likely outcomes, E(X) = ($4 + $8 + $12 + $16) ÷ 4 = $10.

  9. 9. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($10 + $22 + $34 + $46) ÷ 4 = $28.

  10. 10. 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.

  11. 11. A fair 4-sector spinner has equally likely prize values of $21, $35, $49, and $63. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($21 + $35 + $49 + $63) ÷ 4 = $42.

  12. 12. A fair 4-sector spinner has equally likely prize values of $19, $35, $51, and $67. What is the expected value E(X) of one spin?

    $43

    With 4 equally likely outcomes, E(X) = ($19 + $35 + $51 + $67) ÷ 4 = $43.

12 questions · Seed 104732 · 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 $8, $22, $36, and $50. What is the expected value E(X) of one spin?

    4 · $8 · $22 · $36 · Expected value & fair payo…

  2. 2. 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…

  3. 3. 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…

  4. 4. 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…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $5, $17, $29, and $41. What is the expected value E(X) of one spin?

    4 · $5 · $17 · $29 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $26, $36, $46, and $56. What is the expected value E(X) of one spin?

    4 · $26 · $36 · $46 · Expected value & fair payo…

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

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

  9. 9. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?

    4 · $10 · $22 · $34 · Expected value & fair payo…

  10. 10. 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…

  11. 11. A fair 4-sector spinner has equally likely prize values of $21, $35, $49, and $63. What is the expected value E(X) of one spin?

    4 · $21 · $35 · $49 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $19, $35, $51, and $67. What is the expected value E(X) of one spin?

    4 · $19 · $35 · $51 · Expected value & fair payo…
12 questions · Seed 104732 · 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 $8, $22, $36, and $50. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($8 + $22 + $36 + $50) ÷ 4 = $29.

  2. 2. 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.

  3. 3. 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.

  4. 4. 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.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $5, $17, $29, and $41. What is the expected value E(X) of one spin?

    $23

    With 4 equally likely outcomes, E(X) = ($5 + $17 + $29 + $41) ÷ 4 = $23.

  7. 7. A fair 4-sector spinner has equally likely prize values of $26, $36, $46, and $56. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($26 + $36 + $46 + $56) ÷ 4 = $41.

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

    $10

    With 4 equally likely outcomes, E(X) = ($4 + $8 + $12 + $16) ÷ 4 = $10.

  9. 9. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($10 + $22 + $34 + $46) ÷ 4 = $28.

  10. 10. 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.

  11. 11. A fair 4-sector spinner has equally likely prize values of $21, $35, $49, and $63. What is the expected value E(X) of one spin?

    $42

    With 4 equally likely outcomes, E(X) = ($21 + $35 + $49 + $63) ÷ 4 = $42.

  12. 12. A fair 4-sector spinner has equally likely prize values of $19, $35, $51, and $67. What is the expected value E(X) of one spin?

    $43

    With 4 equally likely outcomes, E(X) = ($19 + $35 + $51 + $67) ÷ 4 = $43.

12 questions · Seed 104732 · Age guidance, not curriculum certification