Data and probability · Ages 14–15

Expected value worksheet

Part of: Probability

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Data and probability · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.A game's spinner has 4 equal parts, each number a score, as shown. Spun once, the expected score is .
Answer:
2.A fair die is rolled 180 times. A 1 or more should come up about times.
Answer:
3.A fair die is rolled 156 times. A 6 or more should come up about times.
Answer:
4.In a game, the probability of scoring 0 is 0.2, of scoring 1 is 0.1, and of scoring 29 is 0.7. The expected score is .
Answer:
5.A fair die is rolled: a 6 wins 40 dollars, a 1 wins 8 dollars, anything else nothing. The probability of a 6 is , and the expected prize dollars.
Fill in each blank
Answer:
6.A fair die is rolled: a 6 wins 10 dollars, a 1 wins 20 dollars, anything else nothing. The probability of a 6 is , and the expected prize dollars.
Fill in each blank
Answer:
7.In a game, the probability of scoring 0 is 0.3, of scoring 3 is 0.5, and of scoring 14 is 0.2. The expected score is .
Answer:
8.Two fair coins are tossed together: two heads score 26, exactly one head 10, and two tails 0. What is the expected score?
Answer:
9.Two fair coins are tossed together: two heads score 28, exactly one head 10, and two tails 0. What is the expected score?
Answer:

10.A spinner has 6 equal parts numbered 1 to 6. Spun once, what is the expected number?
- A. 3
- B. 3.5
- C. 6
- D. 7
Choose the right answer
Answer:
11.In a game, scoring 14 and scoring 6 each have probability 12. The expected score is 10.
True or false?
Answer:
12.In a game, scoring 19 and scoring 5 each have probability 12. The expected score is 12.
True or false?
Answer:

13.In a mobile game, each card draw is a legendary card with probability 120. Over 120 draws, legendary cards are expected; to expect 3, about draws are needed.
Fill in each blank
Working:
Answer:
14.A travel insurance policy has a 1200 chance of paying out 29000 dollars on a trip, and pays nothing otherwise. What is the expected payout per policy, in dollars?
Working:
Answer:
15.A charity raffle sells 500 tickets. One first prize of 500 dollars; 20 second prizes of 100 dollars each. The prizes total dollars; the expected prize per ticket is dollars.
Fill in each blank
Working:
Answer:
16.A basketball player scores 60% of free throws, 1 point each. Taking 10 free throws, how many points are expected?
Working:
Answer:
17.A bakery sells 10, 52 or 86 egg tarts a day with probabilities 0.1, 0.4 and 0.5. What is the expected number sold a day?
Working:
Answer:
18.A basketball player scores 90% of free throws, 1 point each. Taking 100 free throws, how many points are expected?
Working:
Answer:

Show the answers and working

Expected value worksheet: Answers and working

1. 5
Each part has probability 14: E = the scores' total × 14 = 20 ÷ 4 = 5.
2. 180
1 or more is 6 outcomes, P = 66; the expected count = 180 × 66 = 180.
3. 26
6 or more is 1 outcomes, P = 16; the expected count = 156 × 16 = 26.
4. 20.4
E = 0 × 0.2 + 1 × 0.1 + 29 × 0.7 = 20.4.
5. 16, 8
E = 40 × 16 + 8 × 16 + 0 × 46 = (40 + 8) ÷ 6 = 8.
6. 16, 5
E = 10 × 16 + 20 × 16 + 0 × 46 = (10 + 20) ÷ 6 = 5.
7. 4.3
E = 0 × 0.3 + 3 × 0.5 + 14 × 0.2 = 4.3.
8. 11.5 points
The four outcomes HH, HT, TH, TT are equally likely: P(two heads) = 14, P(exactly one) = 24 = 12, P(two tails) = 14. E = 26 × 14 + 10 × 12 + 0 × 14 = 11.5.
9. 12 points
The four outcomes HH, HT, TH, TT are equally likely: P(two heads) = 14, P(exactly one) = 24 = 12, P(two tails) = 14. E = 28 × 14 + 10 × 12 + 0 × 14 = 12.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 6, 60
Expected = 120 × 120 = 6; for 3: draws × 120 = 3, so draws = 3 × 20 = 60.
14. 145 dollars
E = 29000 × 1200 + 0 = 145 dollars.
15. 2500, 5
Total = 500 + 20 × 100 = 2500; every ticket is equally likely to win each prize, so E = 2500 ÷ 500 = 5.
16. 6 points
Expected points = 10 × 60% = 6.
17. 64.8 egg tarts
E = 10 × 0.1 + 52 × 0.4 + 86 × 0.5 = 64.8.
18. 90 points
Expected points = 100 × 90% = 90.

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