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, $38, $46, and $54. What is the expected value E(X) of one spin?
4 · $30 · $38 · $46 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $10, $24, $38, and $52. What is the expected value E(X) of one spin?
4 · $10 · $24 · $38 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?
4 · $24 · $38 · $52 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $9, $23, $37, and $51. What is the expected value E(X) of one spin?
4 · $9 · $23 · $37 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?
4 · $10 · $22 · $34 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $23, $27, $31, and $35. What is the expected value E(X) of one spin?
4 · $23 · $27 · $31 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $18, $22, $26, and $30. What is the expected value E(X) of one spin?
4 · $18 · $22 · $26 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $26, $32, $38, and $44. What is the expected value E(X) of one spin?
4 · $26 · $32 · $38 · Expected value & fair payo…
9. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?
4 · $7 · $9 · $11 · Expected value & fair payo…
10. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?
4 · $14 · $24 · $34 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $28, $36, $44, and $52. What is the expected value E(X) of one spin?
4 · $28 · $36 · $44 · Expected value & fair payo…
12. A fair 4-sector spinner has equally likely prize values of $10, $16, $22, and $28. What is the expected value E(X) of one spin?
4 · $10 · $16 · $22 · Expected value & fair payo…

12 questions · Seed 104734 · 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, $38, $46, and $54. What is the expected value E(X) of one spin?
$42
With 4 equally likely outcomes, E(X) = ($30 + $38 + $46 + $54) ÷ 4 = $42.
2. A fair 4-sector spinner has equally likely prize values of $10, $24, $38, and $52. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($10 + $24 + $38 + $52) ÷ 4 = $31.
3. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?
$45
With 4 equally likely outcomes, E(X) = ($24 + $38 + $52 + $66) ÷ 4 = $45.
4. A fair 4-sector spinner has equally likely prize values of $9, $23, $37, and $51. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($9 + $23 + $37 + $51) ÷ 4 = $30.
5. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?
$28
With 4 equally likely outcomes, E(X) = ($10 + $22 + $34 + $46) ÷ 4 = $28.
6. A fair 4-sector spinner has equally likely prize values of $23, $27, $31, and $35. What is the expected value E(X) of one spin?
$29
With 4 equally likely outcomes, E(X) = ($23 + $27 + $31 + $35) ÷ 4 = $29.
7. A fair 4-sector spinner has equally likely prize values of $18, $22, $26, and $30. What is the expected value E(X) of one spin?
$24
With 4 equally likely outcomes, E(X) = ($18 + $22 + $26 + $30) ÷ 4 = $24.
8. A fair 4-sector spinner has equally likely prize values of $26, $32, $38, and $44. What is the expected value E(X) of one spin?
$35
With 4 equally likely outcomes, E(X) = ($26 + $32 + $38 + $44) ÷ 4 = $35.
9. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?
$10
With 4 equally likely outcomes, E(X) = ($7 + $9 + $11 + $13) ÷ 4 = $10.
10. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?
$29
With 4 equally likely outcomes, E(X) = ($14 + $24 + $34 + $44) ÷ 4 = $29.
11. A fair 4-sector spinner has equally likely prize values of $28, $36, $44, and $52. What is the expected value E(X) of one spin?
$40
With 4 equally likely outcomes, E(X) = ($28 + $36 + $44 + $52) ÷ 4 = $40.
12. A fair 4-sector spinner has equally likely prize values of $10, $16, $22, and $28. What is the expected value E(X) of one spin?
$19
With 4 equally likely outcomes, E(X) = ($10 + $16 + $22 + $28) ÷ 4 = $19.

12 questions · Seed 104734 · 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, $38, $46, and $54. What is the expected value E(X) of one spin?
4 · $30 · $38 · $46 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $10, $24, $38, and $52. What is the expected value E(X) of one spin?
4 · $10 · $24 · $38 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?
4 · $24 · $38 · $52 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $9, $23, $37, and $51. What is the expected value E(X) of one spin?
4 · $9 · $23 · $37 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?
4 · $10 · $22 · $34 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $23, $27, $31, and $35. What is the expected value E(X) of one spin?
4 · $23 · $27 · $31 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $18, $22, $26, and $30. What is the expected value E(X) of one spin?
4 · $18 · $22 · $26 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $26, $32, $38, and $44. What is the expected value E(X) of one spin?
4 · $26 · $32 · $38 · Expected value & fair payo…
9. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?
4 · $7 · $9 · $11 · Expected value & fair payo…
10. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?
4 · $14 · $24 · $34 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $28, $36, $44, and $52. What is the expected value E(X) of one spin?
4 · $28 · $36 · $44 · Expected value & fair payo…
12. A fair 4-sector spinner has equally likely prize values of $10, $16, $22, and $28. What is the expected value E(X) of one spin?
4 · $10 · $16 · $22 · Expected value & fair payo…

12 questions · Seed 104734 · 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, $38, $46, and $54. What is the expected value E(X) of one spin?
$42
With 4 equally likely outcomes, E(X) = ($30 + $38 + $46 + $54) ÷ 4 = $42.
2. A fair 4-sector spinner has equally likely prize values of $10, $24, $38, and $52. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($10 + $24 + $38 + $52) ÷ 4 = $31.
3. A fair 4-sector spinner has equally likely prize values of $24, $38, $52, and $66. What is the expected value E(X) of one spin?
$45
With 4 equally likely outcomes, E(X) = ($24 + $38 + $52 + $66) ÷ 4 = $45.
4. A fair 4-sector spinner has equally likely prize values of $9, $23, $37, and $51. What is the expected value E(X) of one spin?
$30
With 4 equally likely outcomes, E(X) = ($9 + $23 + $37 + $51) ÷ 4 = $30.
5. A fair 4-sector spinner has equally likely prize values of $10, $22, $34, and $46. What is the expected value E(X) of one spin?
$28
With 4 equally likely outcomes, E(X) = ($10 + $22 + $34 + $46) ÷ 4 = $28.
6. A fair 4-sector spinner has equally likely prize values of $23, $27, $31, and $35. What is the expected value E(X) of one spin?
$29
With 4 equally likely outcomes, E(X) = ($23 + $27 + $31 + $35) ÷ 4 = $29.
7. A fair 4-sector spinner has equally likely prize values of $18, $22, $26, and $30. What is the expected value E(X) of one spin?
$24
With 4 equally likely outcomes, E(X) = ($18 + $22 + $26 + $30) ÷ 4 = $24.
8. A fair 4-sector spinner has equally likely prize values of $26, $32, $38, and $44. What is the expected value E(X) of one spin?
$35
With 4 equally likely outcomes, E(X) = ($26 + $32 + $38 + $44) ÷ 4 = $35.
9. A fair 4-sector spinner has equally likely prize values of $7, $9, $11, and $13. What is the expected value E(X) of one spin?
$10
With 4 equally likely outcomes, E(X) = ($7 + $9 + $11 + $13) ÷ 4 = $10.
10. A fair 4-sector spinner has equally likely prize values of $14, $24, $34, and $44. What is the expected value E(X) of one spin?
$29
With 4 equally likely outcomes, E(X) = ($14 + $24 + $34 + $44) ÷ 4 = $29.
11. A fair 4-sector spinner has equally likely prize values of $28, $36, $44, and $52. What is the expected value E(X) of one spin?
$40
With 4 equally likely outcomes, E(X) = ($28 + $36 + $44 + $52) ÷ 4 = $40.
12. A fair 4-sector spinner has equally likely prize values of $10, $16, $22, and $28. What is the expected value E(X) of one spin?
$19
With 4 equally likely outcomes, E(X) = ($10 + $16 + $22 + $28) ÷ 4 = $19.

12 questions · Seed 104734 · Age guidance, not curriculum certification