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 $16, $18, $20, and $22. What is the expected value E(X) of one spin?
4 · $16 · $18 · $20 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $20, $34, $48, and $62. What is the expected value E(X) of one spin?
4 · $20 · $34 · $48 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?
4 · $7 · $19 · $31 · Expected value & fair payo…
4. 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…
5. A fair 4-sector spinner has equally likely prize values of $8, $14, $20, and $26. What is the expected value E(X) of one spin?
4 · $8 · $14 · $20 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $5, $11, $17, and $23. What is the expected value E(X) of one spin?
4 · $5 · $11 · $17 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?
4 · $28 · $40 · $52 · Expected value & fair payo…
8. 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…
9. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?
4 · $22 · $32 · $42 · Expected value & fair payo…
10. 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…
11. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?
4 · $16 · $28 · $40 · Expected value & fair payo…
12. 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…

12 questions · Seed 104744 · 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 $16, $18, $20, and $22. What is the expected value E(X) of one spin?
$19
With 4 equally likely outcomes, E(X) = ($16 + $18 + $20 + $22) ÷ 4 = $19.
2. A fair 4-sector spinner has equally likely prize values of $20, $34, $48, and $62. What is the expected value E(X) of one spin?
$41
With 4 equally likely outcomes, E(X) = ($20 + $34 + $48 + $62) ÷ 4 = $41.
3. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?
$25
With 4 equally likely outcomes, E(X) = ($7 + $19 + $31 + $43) ÷ 4 = $25.
4. 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.
5. A fair 4-sector spinner has equally likely prize values of $8, $14, $20, and $26. What is the expected value E(X) of one spin?
$17
With 4 equally likely outcomes, E(X) = ($8 + $14 + $20 + $26) ÷ 4 = $17.
6. A fair 4-sector spinner has equally likely prize values of $5, $11, $17, and $23. What is the expected value E(X) of one spin?
$14
With 4 equally likely outcomes, E(X) = ($5 + $11 + $17 + $23) ÷ 4 = $14.
7. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?
$46
With 4 equally likely outcomes, E(X) = ($28 + $40 + $52 + $64) ÷ 4 = $46.
8. 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.
9. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?
$37
With 4 equally likely outcomes, E(X) = ($22 + $32 + $42 + $52) ÷ 4 = $37.
10. 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.
11. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?
$34
With 4 equally likely outcomes, E(X) = ($16 + $28 + $40 + $52) ÷ 4 = $34.
12. 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.

12 questions · Seed 104744 · 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 $16, $18, $20, and $22. What is the expected value E(X) of one spin?
4 · $16 · $18 · $20 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $20, $34, $48, and $62. What is the expected value E(X) of one spin?
4 · $20 · $34 · $48 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?
4 · $7 · $19 · $31 · Expected value & fair payo…
4. 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…
5. A fair 4-sector spinner has equally likely prize values of $8, $14, $20, and $26. What is the expected value E(X) of one spin?
4 · $8 · $14 · $20 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $5, $11, $17, and $23. What is the expected value E(X) of one spin?
4 · $5 · $11 · $17 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?
4 · $28 · $40 · $52 · Expected value & fair payo…
8. 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…
9. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?
4 · $22 · $32 · $42 · Expected value & fair payo…
10. 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…
11. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?
4 · $16 · $28 · $40 · Expected value & fair payo…
12. 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…

12 questions · Seed 104744 · 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 $16, $18, $20, and $22. What is the expected value E(X) of one spin?
$19
With 4 equally likely outcomes, E(X) = ($16 + $18 + $20 + $22) ÷ 4 = $19.
2. A fair 4-sector spinner has equally likely prize values of $20, $34, $48, and $62. What is the expected value E(X) of one spin?
$41
With 4 equally likely outcomes, E(X) = ($20 + $34 + $48 + $62) ÷ 4 = $41.
3. A fair 4-sector spinner has equally likely prize values of $7, $19, $31, and $43. What is the expected value E(X) of one spin?
$25
With 4 equally likely outcomes, E(X) = ($7 + $19 + $31 + $43) ÷ 4 = $25.
4. 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.
5. A fair 4-sector spinner has equally likely prize values of $8, $14, $20, and $26. What is the expected value E(X) of one spin?
$17
With 4 equally likely outcomes, E(X) = ($8 + $14 + $20 + $26) ÷ 4 = $17.
6. A fair 4-sector spinner has equally likely prize values of $5, $11, $17, and $23. What is the expected value E(X) of one spin?
$14
With 4 equally likely outcomes, E(X) = ($5 + $11 + $17 + $23) ÷ 4 = $14.
7. A fair 4-sector spinner has equally likely prize values of $28, $40, $52, and $64. What is the expected value E(X) of one spin?
$46
With 4 equally likely outcomes, E(X) = ($28 + $40 + $52 + $64) ÷ 4 = $46.
8. 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.
9. A fair 4-sector spinner has equally likely prize values of $22, $32, $42, and $52. What is the expected value E(X) of one spin?
$37
With 4 equally likely outcomes, E(X) = ($22 + $32 + $42 + $52) ÷ 4 = $37.
10. 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.
11. A fair 4-sector spinner has equally likely prize values of $16, $28, $40, and $52. What is the expected value E(X) of one spin?
$34
With 4 equally likely outcomes, E(X) = ($16 + $28 + $40 + $52) ÷ 4 = $34.
12. 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.

12 questions · Seed 104744 · Age guidance, not curriculum certification