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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 $26, $42, $58, and $74. What is the expected value E(X) of one spin?

    4 · $26 · $42 · $58 · Expected value & fair payo…

  2. 2. 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…

  3. 3. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    4 · $26 · $28 · $30 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    4 · $19 · $31 · $43 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $21, $23, $25, and $27. What is the expected value E(X) of one spin?

    4 · $21 · $23 · $25 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $10, $20, $30, and $40. What is the expected value E(X) of one spin?

    4 · $10 · $20 · $30 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $33, $49, and $65. What is the expected value E(X) of one spin?

    4 · $17 · $33 · $49 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $28, $38, $48, and $58. What is the expected value E(X) of one spin?

    4 · $28 · $38 · $48 · 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 $16, $30, $44, and $58. What is the expected value E(X) of one spin?

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

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $17, $25, and $33. What is the expected value E(X) of one spin?

    4 · $9 · $17 · $25 · Expected value & fair payo…
12 questions · Seed 42 · 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 $26, $42, $58, and $74. What is the expected value E(X) of one spin?

    $50

    With 4 equally likely outcomes, E(X) = ($26 + $42 + $58 + $74) ÷ 4 = $50.

  2. 2. 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.

  3. 3. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($26 + $28 + $30 + $32) ÷ 4 = $29.

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($19 + $31 + $43 + $55) ÷ 4 = $37.

  5. 5. A fair 4-sector spinner has equally likely prize values of $21, $23, $25, and $27. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($21 + $23 + $25 + $27) ÷ 4 = $24.

  6. 6. A fair 4-sector spinner has equally likely prize values of $10, $20, $30, and $40. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($10 + $20 + $30 + $40) ÷ 4 = $25.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $33, $49, and $65. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($17 + $33 + $49 + $65) ÷ 4 = $41.

  9. 9. A fair 4-sector spinner has equally likely prize values of $28, $38, $48, and $58. What is the expected value E(X) of one spin?

    $43

    With 4 equally likely outcomes, E(X) = ($28 + $38 + $48 + $58) ÷ 4 = $43.

  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 $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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $17, $25, and $33. What is the expected value E(X) of one spin?

    $21

    With 4 equally likely outcomes, E(X) = ($9 + $17 + $25 + $33) ÷ 4 = $21.

12 questions · Seed 42 · 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 $26, $42, $58, and $74. What is the expected value E(X) of one spin?

    4 · $26 · $42 · $58 · Expected value & fair payo…

  2. 2. 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…

  3. 3. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    4 · $26 · $28 · $30 · Expected value & fair payo…

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    4 · $19 · $31 · $43 · Expected value & fair payo…

  5. 5. A fair 4-sector spinner has equally likely prize values of $21, $23, $25, and $27. What is the expected value E(X) of one spin?

    4 · $21 · $23 · $25 · Expected value & fair payo…

  6. 6. A fair 4-sector spinner has equally likely prize values of $10, $20, $30, and $40. What is the expected value E(X) of one spin?

    4 · $10 · $20 · $30 · Expected value & fair payo…

  7. 7. 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…

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $33, $49, and $65. What is the expected value E(X) of one spin?

    4 · $17 · $33 · $49 · Expected value & fair payo…

  9. 9. A fair 4-sector spinner has equally likely prize values of $28, $38, $48, and $58. What is the expected value E(X) of one spin?

    4 · $28 · $38 · $48 · 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 $16, $30, $44, and $58. What is the expected value E(X) of one spin?

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

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $17, $25, and $33. What is the expected value E(X) of one spin?

    4 · $9 · $17 · $25 · Expected value & fair payo…
12 questions · Seed 42 · 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 $26, $42, $58, and $74. What is the expected value E(X) of one spin?

    $50

    With 4 equally likely outcomes, E(X) = ($26 + $42 + $58 + $74) ÷ 4 = $50.

  2. 2. 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.

  3. 3. A fair 4-sector spinner has equally likely prize values of $26, $28, $30, and $32. What is the expected value E(X) of one spin?

    $29

    With 4 equally likely outcomes, E(X) = ($26 + $28 + $30 + $32) ÷ 4 = $29.

  4. 4. A fair 4-sector spinner has equally likely prize values of $19, $31, $43, and $55. What is the expected value E(X) of one spin?

    $37

    With 4 equally likely outcomes, E(X) = ($19 + $31 + $43 + $55) ÷ 4 = $37.

  5. 5. A fair 4-sector spinner has equally likely prize values of $21, $23, $25, and $27. What is the expected value E(X) of one spin?

    $24

    With 4 equally likely outcomes, E(X) = ($21 + $23 + $25 + $27) ÷ 4 = $24.

  6. 6. A fair 4-sector spinner has equally likely prize values of $10, $20, $30, and $40. What is the expected value E(X) of one spin?

    $25

    With 4 equally likely outcomes, E(X) = ($10 + $20 + $30 + $40) ÷ 4 = $25.

  7. 7. 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.

  8. 8. A fair 4-sector spinner has equally likely prize values of $17, $33, $49, and $65. What is the expected value E(X) of one spin?

    $41

    With 4 equally likely outcomes, E(X) = ($17 + $33 + $49 + $65) ÷ 4 = $41.

  9. 9. A fair 4-sector spinner has equally likely prize values of $28, $38, $48, and $58. What is the expected value E(X) of one spin?

    $43

    With 4 equally likely outcomes, E(X) = ($28 + $38 + $48 + $58) ÷ 4 = $43.

  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 $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.

  12. 12. A fair 4-sector spinner has equally likely prize values of $9, $17, $25, and $33. What is the expected value E(X) of one spin?

    $21

    With 4 equally likely outcomes, E(X) = ($9 + $17 + $25 + $33) ÷ 4 = $21.

12 questions · Seed 42 · Age guidance, not curriculum certification