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Grade 11 · Math · Algebra 2

11th grade Games of chance: expected payoff, the better bet and fair decisions worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Games of chance: expected payoff, the better bet and fair decisions

Grade 11 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

  1. At the school fair's free ring toss, each throw gets a prize with chance 0.15. If 240 children each throw once, how many prizes should Jun expect to hand out?

  2. At a free bean-bag toss, each throw has a 0.35 chance of landing in the basket. How many of 160 throws should Luz expect to land in the basket?

  3. In a drop test, each phone case has a 0.04 chance of cracking. How many of 2,500 cases should Milo expect to crack?

  4. Read this first

    Equally likely outcomes

    HH, HT, TH, TT.

  5. Noah and a friend toss two fair coins. If the coins match, Noah goes first; if not, the friend does. Is the rule fair?

    • Not fair: matching has a chance of 1/4
    • Fair: each has a chance of 1/2
    • Not fair: matching has a chance of 2/3

  6. Pia and two friends toss two fair coins: two heads picks Pia, two tails picks one friend, and one of each picks the other. Is the rule fair?

    • Fair: each has a chance of 1/3
    • Fair: each has a chance of 1/4
    • Not fair: one of each has a chance of 1/2

  7. 1, 2, 3, 4, 5, 6. Ren and a friend roll a fair number cube. A 1 or 2 means Ren goes first; 3, 4, 5 or 6 means the friend does. Is the rule fair?

    • Not fair: Ren has a chance of 2/3
    • Fair: there are two groups, so each has a chance of 1/2
    • Not fair: the friend has a chance of 2/3

  8. Red, blue, yellow, green. Tala and a friend spin a spinner with 4 equal sections: red, blue, yellow and green. Red means Tala goes first; any other color means the friend does. Is the rule fair?

    • Fair: red or not red, so each has a chance of 1/2
    • Not fair: Tala has a chance of 3/4
    • Not fair: the friend has a chance of 3/4

  9. Use this

    Table: no repair, screen fix, new phone; cost = $0, $120, $400; chance = 0.75, 0.2, 0.05; cost × chance = $0, $24, $20.

  10. Zee's teacher lists a year of phone repair costs and their chances. What is the expected repair cost for the year?

  11. Use this

    Table: no repair, flat tire, new wheel; cost = $0, $30, $90; chance = 0.6, 0.3, 0.1; cost × chance = $0, $9, $9.

  12. A bike shop owner shows Esme a month of repair costs for one rental bike. What is the expected repair cost for the month?

  13. Table

    No repair, new keys, new screen, new laptop; cost = $0, $80, $250, $600; chance = 0.7, 0.2, 0.08, 0.02; cost × chance = $0, $16, $20, $12. Dot plot: number line $0 to $600, each stack as tall as its chance.

  14. The school office shows Jun a year of repair costs for one class laptop. What is the expected repair cost for the year?

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11th grade Games of chance: expected payoff, the better bet and fair decisions worksheet – printable
Print: 123456

About this worksheet

Expected value for decisions, and fair ways to choose. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find an expected count, cost or earning, including a fixed fee or cost.
  • I can choose between two options by expected value, not by the best or worst outcome.
  • I can tell whether a rule for picking is fair by counting equally likely outcomes.

Standard: S-MD.B.5 (+), S-MD.B.6 (+), S-MD.B.7 (+)

Words to know

expected value: The balance point of the amounts, each weighted by its chance.

expected count: Number of tries × the chance.

fair rule: A rule that gives every person the same chance.

equally likely outcomes: Results that each have the same chance, like HT and TH.

break-even chance: The chance that makes two options' expected values equal.

Common mistakes

Multiplied by the chance of a miss instead of a hit.

Read a chance such as 0.15 as 15 items. Multiply the number of tries by the chance together.

Treated groups of outcomes (such as "one of each" or a sum) as equally likely. List every outcome together and count each group.

What to say

Ask: which chance goes with the thing we are counting?

Questions parents ask

What is the most common mistake with games of chance: expected payoff, the better bet and fair decisions?

Multiplied by the chance of a miss instead of a hit.

How can I help my child with games of chance: expected payoff, the better bet and fair decisions?

Ask: which chance goes with the thing we are counting?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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