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 $11, $27, $43, and $59. What is the expected value E(X) of one spin?
4 · $11 · $27 · $43 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?
4 · $18 · $32 · $46 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $28, $30, $32, and $34. What is the expected value E(X) of one spin?
4 · $28 · $30 · $32 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?
4 · $17 · $19 · $21 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $18, $24, $30, and $36. What is the expected value E(X) of one spin?
4 · $18 · $24 · $30 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?
4 · $22 · $28 · $34 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?
4 · $22 · $24 · $26 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $10, $12, $14, and $16. What is the expected value E(X) of one spin?
4 · $10 · $12 · $14 · Expected value & fair payo…
9. 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…
10. A fair 4-sector spinner has equally likely prize values of $11, $15, $19, and $23. What is the expected value E(X) of one spin?
4 · $11 · $15 · $19 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $3, $15, $27, and $39. What is the expected value E(X) of one spin?
4 · $3 · $15 · $27 · Expected value & fair payo…
12. 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…

12 questions · Seed 104736 · 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 $11, $27, $43, and $59. What is the expected value E(X) of one spin?
$35
With 4 equally likely outcomes, E(X) = ($11 + $27 + $43 + $59) ÷ 4 = $35.
2. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?
$39
With 4 equally likely outcomes, E(X) = ($18 + $32 + $46 + $60) ÷ 4 = $39.
3. A fair 4-sector spinner has equally likely prize values of $28, $30, $32, and $34. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($28 + $30 + $32 + $34) ÷ 4 = $31.
4. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?
$20
With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.
5. A fair 4-sector spinner has equally likely prize values of $18, $24, $30, and $36. What is the expected value E(X) of one spin?
$27
With 4 equally likely outcomes, E(X) = ($18 + $24 + $30 + $36) ÷ 4 = $27.
6. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($22 + $28 + $34 + $40) ÷ 4 = $31.
7. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?
$25
With 4 equally likely outcomes, E(X) = ($22 + $24 + $26 + $28) ÷ 4 = $25.
8. A fair 4-sector spinner has equally likely prize values of $10, $12, $14, and $16. What is the expected value E(X) of one spin?
$13
With 4 equally likely outcomes, E(X) = ($10 + $12 + $14 + $16) ÷ 4 = $13.
9. 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.
10. A fair 4-sector spinner has equally likely prize values of $11, $15, $19, and $23. What is the expected value E(X) of one spin?
$17
With 4 equally likely outcomes, E(X) = ($11 + $15 + $19 + $23) ÷ 4 = $17.
11. A fair 4-sector spinner has equally likely prize values of $3, $15, $27, and $39. What is the expected value E(X) of one spin?
$21
With 4 equally likely outcomes, E(X) = ($3 + $15 + $27 + $39) ÷ 4 = $21.
12. 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.

12 questions · Seed 104736 · 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 $11, $27, $43, and $59. What is the expected value E(X) of one spin?
4 · $11 · $27 · $43 · Expected value & fair payo…
2. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?
4 · $18 · $32 · $46 · Expected value & fair payo…
3. A fair 4-sector spinner has equally likely prize values of $28, $30, $32, and $34. What is the expected value E(X) of one spin?
4 · $28 · $30 · $32 · Expected value & fair payo…
4. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?
4 · $17 · $19 · $21 · Expected value & fair payo…
5. A fair 4-sector spinner has equally likely prize values of $18, $24, $30, and $36. What is the expected value E(X) of one spin?
4 · $18 · $24 · $30 · Expected value & fair payo…
6. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?
4 · $22 · $28 · $34 · Expected value & fair payo…
7. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?
4 · $22 · $24 · $26 · Expected value & fair payo…
8. A fair 4-sector spinner has equally likely prize values of $10, $12, $14, and $16. What is the expected value E(X) of one spin?
4 · $10 · $12 · $14 · Expected value & fair payo…
9. 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…
10. A fair 4-sector spinner has equally likely prize values of $11, $15, $19, and $23. What is the expected value E(X) of one spin?
4 · $11 · $15 · $19 · Expected value & fair payo…
11. A fair 4-sector spinner has equally likely prize values of $3, $15, $27, and $39. What is the expected value E(X) of one spin?
4 · $3 · $15 · $27 · Expected value & fair payo…
12. 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…

12 questions · Seed 104736 · 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 $11, $27, $43, and $59. What is the expected value E(X) of one spin?
$35
With 4 equally likely outcomes, E(X) = ($11 + $27 + $43 + $59) ÷ 4 = $35.
2. A fair 4-sector spinner has equally likely prize values of $18, $32, $46, and $60. What is the expected value E(X) of one spin?
$39
With 4 equally likely outcomes, E(X) = ($18 + $32 + $46 + $60) ÷ 4 = $39.
3. A fair 4-sector spinner has equally likely prize values of $28, $30, $32, and $34. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($28 + $30 + $32 + $34) ÷ 4 = $31.
4. A fair 4-sector spinner has equally likely prize values of $17, $19, $21, and $23. What is the expected value E(X) of one spin?
$20
With 4 equally likely outcomes, E(X) = ($17 + $19 + $21 + $23) ÷ 4 = $20.
5. A fair 4-sector spinner has equally likely prize values of $18, $24, $30, and $36. What is the expected value E(X) of one spin?
$27
With 4 equally likely outcomes, E(X) = ($18 + $24 + $30 + $36) ÷ 4 = $27.
6. A fair 4-sector spinner has equally likely prize values of $22, $28, $34, and $40. What is the expected value E(X) of one spin?
$31
With 4 equally likely outcomes, E(X) = ($22 + $28 + $34 + $40) ÷ 4 = $31.
7. A fair 4-sector spinner has equally likely prize values of $22, $24, $26, and $28. What is the expected value E(X) of one spin?
$25
With 4 equally likely outcomes, E(X) = ($22 + $24 + $26 + $28) ÷ 4 = $25.
8. A fair 4-sector spinner has equally likely prize values of $10, $12, $14, and $16. What is the expected value E(X) of one spin?
$13
With 4 equally likely outcomes, E(X) = ($10 + $12 + $14 + $16) ÷ 4 = $13.
9. 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.
10. A fair 4-sector spinner has equally likely prize values of $11, $15, $19, and $23. What is the expected value E(X) of one spin?
$17
With 4 equally likely outcomes, E(X) = ($11 + $15 + $19 + $23) ÷ 4 = $17.
11. A fair 4-sector spinner has equally likely prize values of $3, $15, $27, and $39. What is the expected value E(X) of one spin?
$21
With 4 equally likely outcomes, E(X) = ($3 + $15 + $27 + $39) ÷ 4 = $21.
12. 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.

12 questions · Seed 104736 · Age guidance, not curriculum certification