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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 $15, $31, $47, and $63. What is the expected value E(X) of one spin?

    4 · $15 · $31 · $47 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    4 · $14 · $26 · $38 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    4 · $13 · $19 · $25 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $4, $6, $8, and $10. What is the expected value E(X) of one spin?

    4 · $4 · $6 · $8 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?

    4 · $18 · $32 · $46 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $18, $30, $42, and $54. What is the expected value E(X) of one spin?

    4 · $18 · $30 · $42 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    4 · $17 · $25 · $33 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    4 · $17 · $19 · $21 · Expected value & fair payo…

  10. 10. 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…

  11. 11. A fair 4-sector spinner has equally likely prize values of $4, $10, $16, and $22. What is the expected value E(X) of one spin?

    4 · $4 · $10 · $16 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    4 · $21 · $27 · $33 · Expected value & fair payo…
12 questions · Seed 104740 · 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 $15, $31, $47, and $63. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($15 + $31 + $47 + $63) ÷ 4 = $39.

  2. 2. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($14 + $26 + $38 + $50) ÷ 4 = $32.

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($13 + $19 + $25 + $31) ÷ 4 = $22.

  4. 4. A fair 4-sector spinner has equally likely prize values of $4, $6, $8, and $10. What is the expected value E(X) of one spin?

    $7

    With 4 equally likely outcomes, E(X) = ($4 + $6 + $8 + $10) ÷ 4 = $7.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($18 + $32 + $46 + $60) ÷ 4 = $39.

  7. 7. A fair 4-sector spinner has equally likely prize values of $18, $30, $42, and $54. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($18 + $30 + $42 + $54) ÷ 4 = $36.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($17 + $25 + $33 + $41) ÷ 4 = $29.

  9. 9. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.

  10. 10. 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.

  11. 11. A fair 4-sector spinner has equally likely prize values of $4, $10, $16, and $22. What is the expected value E(X) of one spin?

    $13

    With 4 equally likely outcomes, E(X) = ($4 + $10 + $16 + $22) ÷ 4 = $13.

  12. 12. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($21 + $27 + $33 + $39) ÷ 4 = $30.

12 questions · Seed 104740 · 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 $15, $31, $47, and $63. What is the expected value E(X) of one spin?

    4 · $15 · $31 · $47 · Expected value & fair payo…

  2. 2. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    4 · $14 · $26 · $38 · Expected value & fair payo…

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    4 · $13 · $19 · $25 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $4, $6, $8, and $10. What is the expected value E(X) of one spin?

    4 · $4 · $6 · $8 · Expected value & fair payo…

  5. 5. 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…

  6. 6. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?

    4 · $18 · $32 · $46 · Expected value & fair payo…

  7. 7. A fair 4-sector spinner has equally likely prize values of $18, $30, $42, and $54. What is the expected value E(X) of one spin?

    4 · $18 · $30 · $42 · Expected value & fair payo…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    4 · $17 · $25 · $33 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    4 · $17 · $19 · $21 · Expected value & fair payo…

  10. 10. 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…

  11. 11. A fair 4-sector spinner has equally likely prize values of $4, $10, $16, and $22. What is the expected value E(X) of one spin?

    4 · $4 · $10 · $16 · Expected value & fair payo…

  12. 12. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    4 · $21 · $27 · $33 · Expected value & fair payo…
12 questions · Seed 104740 · 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 $15, $31, $47, and $63. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($15 + $31 + $47 + $63) ÷ 4 = $39.

  2. 2. A fair 4-sector spinner has equally likely prize values of $14, $26, $38, and $50. What is the expected value E(X) of one spin?

    $32

    With 4 equally likely outcomes, E(X) = ($14 + $26 + $38 + $50) ÷ 4 = $32.

  3. 3. A fair 4-sector spinner has equally likely prize values of $13, $19, $25, and $31. What is the expected value E(X) of one spin?

    $22

    With 4 equally likely outcomes, E(X) = ($13 + $19 + $25 + $31) ÷ 4 = $22.

  4. 4. A fair 4-sector spinner has equally likely prize values of $4, $6, $8, and $10. What is the expected value E(X) of one spin?

    $7

    With 4 equally likely outcomes, E(X) = ($4 + $6 + $8 + $10) ÷ 4 = $7.

  5. 5. 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.

  6. 6. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?

    $39

    With 4 equally likely outcomes, E(X) = ($18 + $32 + $46 + $60) ÷ 4 = $39.

  7. 7. A fair 4-sector spinner has equally likely prize values of $18, $30, $42, and $54. What is the expected value E(X) of one spin?

    $36

    With 4 equally likely outcomes, E(X) = ($18 + $30 + $42 + $54) ÷ 4 = $36.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $25, $33, and $41. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($17 + $25 + $33 + $41) ÷ 4 = $29.

  9. 9. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?

    $20

    With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.

  10. 10. 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.

  11. 11. A fair 4-sector spinner has equally likely prize values of $4, $10, $16, and $22. What is the expected value E(X) of one spin?

    $13

    With 4 equally likely outcomes, E(X) = ($4 + $10 + $16 + $22) ÷ 4 = $13.

  12. 12. A fair 4-sector spinner has equally likely prize values of $21, $27, $33, and $39. What is the expected value E(X) of one spin?

    $30

    With 4 equally likely outcomes, E(X) = ($21 + $27 + $33 + $39) ÷ 4 = $30.

12 questions · Seed 104740 · Age guidance, not curriculum certification