Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 $29, $33, $37, and $41. What is the expected value E(X) of one spin?

    4 · $29 · $33 · $37 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $3, $7, $11, and $15. What is the expected value E(X) of one spin?

    4 · $3 · $7 · $11 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $44, $58, and $72. What is the expected value E(X) of one spin?

    4 · $30 · $44 · $58 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    4 · $23 · $35 · $47 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    4 · $30 · $36 · $42 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $20, $32, $44, and $56. What is the expected value E(X) of one spin?

    4 · $20 · $32 · $44 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    4 · $11 · $25 · $39 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?

    4 · $7 · $21 · $35 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $30, $44, and $58. What is the expected value E(X) of one spin?

    4 · $16 · $30 · $44 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $31, $45, and $59. What is the expected value E(X) of one spin?

    4 · $17 · $31 · $45 · Expected value & fair payo…
12 questions · Seed 104733 · 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 $29, $33, $37, and $41. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($29 + $33 + $37 + $41) ÷ 4 = $35.

  2. 2. A fair 4-sector spinner has equally likely prize values of $3, $7, $11, and $15. What is the expected value E(X) of one spin?

    $9

    With 4 equally likely outcomes, E(X) = ($3 + $7 + $11 + $15) ÷ 4 = $9.

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $44, $58, and $72. What is the expected value E(X) of one spin?

    $51

    With 4 equally likely outcomes, E(X) = ($30 + $44 + $58 + $72) ÷ 4 = $51.

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($23 + $35 + $47 + $59) ÷ 4 = $41.

  5. 5. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($30 + $36 + $42 + $48) ÷ 4 = $39.

  6. 6. A fair 4-sector spinner has equally likely prize values of $20, $32, $44, and $56. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($20 + $32 + $44 + $56) ÷ 4 = $38.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($11 + $25 + $39 + $53) ÷ 4 = $32.

  9. 9. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($7 + $21 + $35 + $49) ÷ 4 = $28.

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $30, $44, and $58. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($16 + $30 + $44 + $58) ÷ 4 = $37.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $31, $45, and $59. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($17 + $31 + $45 + $59) ÷ 4 = $38.

12 questions · Seed 104733 · 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 $29, $33, $37, and $41. What is the expected value E(X) of one spin?

    4 · $29 · $33 · $37 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $3, $7, $11, and $15. What is the expected value E(X) of one spin?

    4 · $3 · $7 · $11 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $44, $58, and $72. What is the expected value E(X) of one spin?

    4 · $30 · $44 · $58 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    4 · $23 · $35 · $47 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    4 · $30 · $36 · $42 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $20, $32, $44, and $56. What is the expected value E(X) of one spin?

    4 · $20 · $32 · $44 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    4 · $11 · $25 · $39 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?

    4 · $7 · $21 · $35 · Expected value & fair payo…

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $30, $44, and $58. What is the expected value E(X) of one spin?

    4 · $16 · $30 · $44 · Expected value & fair payo…

  11. 11. 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…

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $31, $45, and $59. What is the expected value E(X) of one spin?

    4 · $17 · $31 · $45 · Expected value & fair payo…
12 questions · Seed 104733 · 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 $29, $33, $37, and $41. What is the expected value E(X) of one spin?

    $35

    With 4 equally likely outcomes, E(X) = ($29 + $33 + $37 + $41) ÷ 4 = $35.

  2. 2. A fair 4-sector spinner has equally likely prize values of $3, $7, $11, and $15. What is the expected value E(X) of one spin?

    $9

    With 4 equally likely outcomes, E(X) = ($3 + $7 + $11 + $15) ÷ 4 = $9.

  3. 3. A fair 4-sector spinner has equally likely prize values of $30, $44, $58, and $72. What is the expected value E(X) of one spin?

    $51

    With 4 equally likely outcomes, E(X) = ($30 + $44 + $58 + $72) ÷ 4 = $51.

  4. 4. A fair 4-sector spinner has equally likely prize values of $23, $35, $47, and $59. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($23 + $35 + $47 + $59) ÷ 4 = $41.

  5. 5. A fair 4-sector spinner has equally likely prize values of $30, $36, $42, and $48. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($30 + $36 + $42 + $48) ÷ 4 = $39.

  6. 6. A fair 4-sector spinner has equally likely prize values of $20, $32, $44, and $56. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($20 + $32 + $44 + $56) ÷ 4 = $38.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $11, $25, $39, and $53. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($11 + $25 + $39 + $53) ÷ 4 = $32.

  9. 9. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?

    $28

    With 4 equally likely outcomes, E(X) = ($7 + $21 + $35 + $49) ÷ 4 = $28.

  10. 10. A fair 4-sector spinner has equally likely prize values of $16, $30, $44, and $58. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($16 + $30 + $44 + $58) ÷ 4 = $37.

  11. 11. 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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $17, $31, $45, and $59. What is the expected value E(X) of one spin?

    $38

    With 4 equally likely outcomes, E(X) = ($17 + $31 + $45 + $59) ÷ 4 = $38.

12 questions · Seed 104733 · Age guidance, not curriculum certification