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 $6, $10, $14, and $18. What is the expected value E(X) of one spin?
4 · $6 · $10 · $14 · Expected value & fair payo…
2. 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…
3. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?
4 · $29 · $31 · $33 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $3, $13, $23, and $33. What is the expected value E(X) of one spin?
4 · $3 · $13 · $23 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?
4 · $7 · $21 · $35 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?
4 · $30 · $34 · $38 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $20, $24, $28, and $32. What is the expected value E(X) of one spin?
4 · $20 · $24 · $28 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $26, $40, $54, and $68. What is the expected value E(X) of one spin?
4 · $26 · $40 · $54 · Expected value & fair payo…
9. 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…
10. 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…
11. 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. A fair 4-sector spinner has equally likely prize values of $4, $8, $12, and $16. What is the expected value E(X) of one spin?
4 · $4 · $8 · $12 · Expected value & fair payo…

12 questions · Seed 104741 · 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 $6, $10, $14, and $18. What is the expected value E(X) of one spin?
$12
With 4 equally likely outcomes, E(X) = ($6 + $10 + $14 + $18) ÷ 4 = $12.
2. 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.
3. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?
$32
With 4 equally likely outcomes, E(X) = ($29 + $31 + $33 + $35) ÷ 4 = $32.
4. A fair 4-sector spinner has equally likely prize values of $3, $13, $23, and $33. What is the expected value E(X) of one spin?
$18
With 4 equally likely outcomes, E(X) = ($3 + $13 + $23 + $33) ÷ 4 = $18.
5. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?
$28
With 4 equally likely outcomes, E(X) = ($7 + $21 + $35 + $49) ÷ 4 = $28.
6. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?
$36
With 4 equally likely outcomes, E(X) = ($30 + $34 + $38 + $42) ÷ 4 = $36.
7. A fair 4-sector spinner has equally likely prize values of $20, $24, $28, and $32. What is the expected value E(X) of one spin?
$26
With 4 equally likely outcomes, E(X) = ($20 + $24 + $28 + $32) ÷ 4 = $26.
8. A fair 4-sector spinner has equally likely prize values of $26, $40, $54, and $68. What is the expected value E(X) of one spin?
$47
With 4 equally likely outcomes, E(X) = ($26 + $40 + $54 + $68) ÷ 4 = $47.
9. 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.
10. 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.
11. 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. A fair 4-sector spinner has equally likely prize values of $4, $8, $12, and $16. What is the expected value E(X) of one spin?
$10
With 4 equally likely outcomes, E(X) = ($4 + $8 + $12 + $16) ÷ 4 = $10.

12 questions · Seed 104741 · 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 $6, $10, $14, and $18. What is the expected value E(X) of one spin?
4 · $6 · $10 · $14 · Expected value & fair payo…
2. 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…
3. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?
4 · $29 · $31 · $33 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $3, $13, $23, and $33. What is the expected value E(X) of one spin?
4 · $3 · $13 · $23 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?
4 · $7 · $21 · $35 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?
4 · $30 · $34 · $38 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $20, $24, $28, and $32. What is the expected value E(X) of one spin?
4 · $20 · $24 · $28 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $26, $40, $54, and $68. What is the expected value E(X) of one spin?
4 · $26 · $40 · $54 · Expected value & fair payo…
9. 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…
10. 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…
11. 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. A fair 4-sector spinner has equally likely prize values of $4, $8, $12, and $16. What is the expected value E(X) of one spin?
4 · $4 · $8 · $12 · Expected value & fair payo…

12 questions · Seed 104741 · 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 $6, $10, $14, and $18. What is the expected value E(X) of one spin?
$12
With 4 equally likely outcomes, E(X) = ($6 + $10 + $14 + $18) ÷ 4 = $12.
2. 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.
3. A fair 4-sector spinner has equally likely prize values of $29, $31, $33, and $35. What is the expected value E(X) of one spin?
$32
With 4 equally likely outcomes, E(X) = ($29 + $31 + $33 + $35) ÷ 4 = $32.
4. A fair 4-sector spinner has equally likely prize values of $3, $13, $23, and $33. What is the expected value E(X) of one spin?
$18
With 4 equally likely outcomes, E(X) = ($3 + $13 + $23 + $33) ÷ 4 = $18.
5. A fair 4-sector spinner has equally likely prize values of $7, $21, $35, and $49. What is the expected value E(X) of one spin?
$28
With 4 equally likely outcomes, E(X) = ($7 + $21 + $35 + $49) ÷ 4 = $28.
6. A fair 4-sector spinner has equally likely prize values of $30, $34, $38, and $42. What is the expected value E(X) of one spin?
$36
With 4 equally likely outcomes, E(X) = ($30 + $34 + $38 + $42) ÷ 4 = $36.
7. A fair 4-sector spinner has equally likely prize values of $20, $24, $28, and $32. What is the expected value E(X) of one spin?
$26
With 4 equally likely outcomes, E(X) = ($20 + $24 + $28 + $32) ÷ 4 = $26.
8. A fair 4-sector spinner has equally likely prize values of $26, $40, $54, and $68. What is the expected value E(X) of one spin?
$47
With 4 equally likely outcomes, E(X) = ($26 + $40 + $54 + $68) ÷ 4 = $47.
9. 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.
10. 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.
11. 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. A fair 4-sector spinner has equally likely prize values of $4, $8, $12, and $16. What is the expected value E(X) of one spin?
$10
With 4 equally likely outcomes, E(X) = ($4 + $8 + $12 + $16) ÷ 4 = $10.

12 questions · Seed 104741 · Age guidance, not curriculum certification