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. 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…
2. 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…
3. A fair 4-sector spinner has equally likely prize values of $21, $29, $37, and $45. What is the expected value E(X) of one spin?
4 · $21 · $29 · $37 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $8, $16, $24, and $32. What is the expected value E(X) of one spin?
4 · $8 · $16 · $24 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $6, $22, $38, and $54. What is the expected value E(X) of one spin?
4 · $6 · $22 · $38 · Expected value & fair payo…
6. 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…
7. A fair 4-sector spinner has equally likely prize values of $7, $17, $27, and $37. What is the expected value E(X) of one spin?
4 · $7 · $17 · $27 · Expected value & fair payo…
8. 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…
9. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?
4 · $9 · $19 · $29 · Expected value & fair payo…
10. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?
4 · $30 · $32 · $34 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?
4 · $27 · $31 · $35 · Expected value & fair payo…
12. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?
4 · $12 · $24 · $36 · Expected value & fair payo…

12 questions · Seed 104739 · 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. 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.
2. 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.
3. A fair 4-sector spinner has equally likely prize values of $21, $29, $37, and $45. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($21 + $29 + $37 + $45) ÷ 4 = $33.
4. A fair 4-sector spinner has equally likely prize values of $8, $16, $24, and $32. What is the expected value E(X) of one spin?
$20
With 4 equally likely outcomes, E(X) = ($8 + $16 + $24 + $32) ÷ 4 = $20.
5. A fair 4-sector spinner has equally likely prize values of $6, $22, $38, and $54. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($6 + $22 + $38 + $54) ÷ 4 = $30.
6. 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.
7. A fair 4-sector spinner has equally likely prize values of $7, $17, $27, and $37. What is the expected value E(X) of one spin?
$22
With 4 equally likely outcomes, E(X) = ($7 + $17 + $27 + $37) ÷ 4 = $22.
8. 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.
9. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?
$24
With 4 equally likely outcomes, E(X) = ($9 + $19 + $29 + $39) ÷ 4 = $24.
10. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.
11. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($27 + $31 + $35 + $39) ÷ 4 = $33.
12. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($12 + $24 + $36 + $48) ÷ 4 = $30.

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Expected value & fair payouts

Take your time. Show your thinking.

1. 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…
2. 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…
3. A fair 4-sector spinner has equally likely prize values of $21, $29, $37, and $45. What is the expected value E(X) of one spin?
4 · $21 · $29 · $37 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $8, $16, $24, and $32. What is the expected value E(X) of one spin?
4 · $8 · $16 · $24 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $6, $22, $38, and $54. What is the expected value E(X) of one spin?
4 · $6 · $22 · $38 · Expected value & fair payo…
6. 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…
7. A fair 4-sector spinner has equally likely prize values of $7, $17, $27, and $37. What is the expected value E(X) of one spin?
4 · $7 · $17 · $27 · Expected value & fair payo…
8. 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…
9. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?
4 · $9 · $19 · $29 · Expected value & fair payo…
10. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?
4 · $30 · $32 · $34 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?
4 · $27 · $31 · $35 · Expected value & fair payo…
12. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?
4 · $12 · $24 · $36 · Expected value & fair payo…

12 questions · Seed 104739 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Expected value & fair payouts

Answers and reasoning. Review before teaching.

1. 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.
2. 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.
3. A fair 4-sector spinner has equally likely prize values of $21, $29, $37, and $45. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($21 + $29 + $37 + $45) ÷ 4 = $33.
4. A fair 4-sector spinner has equally likely prize values of $8, $16, $24, and $32. What is the expected value E(X) of one spin?
$20
With 4 equally likely outcomes, E(X) = ($8 + $16 + $24 + $32) ÷ 4 = $20.
5. A fair 4-sector spinner has equally likely prize values of $6, $22, $38, and $54. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($6 + $22 + $38 + $54) ÷ 4 = $30.
6. 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.
7. A fair 4-sector spinner has equally likely prize values of $7, $17, $27, and $37. What is the expected value E(X) of one spin?
$22
With 4 equally likely outcomes, E(X) = ($7 + $17 + $27 + $37) ÷ 4 = $22.
8. 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.
9. A fair 4-sector spinner has equally likely prize values of $9, $19, $29, and $39. What is the expected value E(X) of one spin?
$24
With 4 equally likely outcomes, E(X) = ($9 + $19 + $29 + $39) ÷ 4 = $24.
10. A fair 4-sector spinner has equally likely prize values of $30, $32, $34, and $36. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($30 + $32 + $34 + $36) ÷ 4 = $33.
11. A fair 4-sector spinner has equally likely prize values of $27, $31, $35, and $39. What is the expected value E(X) of one spin?
$33
With 4 equally likely outcomes, E(X) = ($27 + $31 + $35 + $39) ÷ 4 = $33.
12. A fair 4-sector spinner has equally likely prize values of $12, $24, $36, and $48. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($12 + $24 + $36 + $48) ÷ 4 = $30.

12 questions · Seed 104739 · Age guidance, not curriculum certification