Grade 11 · Math · Algebra 2

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

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

Grade 11 Math Worksheet - Challenge Me

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

$500 if dry, $100 if rainy. Indoor sale: $340 for sure. Kira's club can hold an outdoor fair or an indoor sale. What chance of dry weather makes the two expected earnings equal?
$800 if it is a home game, $200 if not. At school: $350 for sure. Luz's club can sell snacks at the next game or at school. What chance of a home game makes the two expected earnings equal?
$1,000 if sunny, $250 if not. Hall sale: $400 for sure. Noah's club can hold a garden sale or a hall sale. What chance of sun makes the two expected earnings equal?
A club makes 120 gift boxes at $3 each. Each sells for $8 with chance 0.75; unsold boxes are given to a shelter. What expected profit for the batch does Ren find?
A factory makes 500 bulbs at $1.20 each. A bulb that passes (chance 0.96) sells for $4; one that fails is thrown out. What expected profit for the batch does Tala find?
Ripe, bruised, spoiled; price = $7, $3, $0; chance = 0.8, 0.15, 0.05. A farm stand grows 80 melons at $2 each. The table gives each melon's price and chance. What expected profit for the batch does Zee find?
7.
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT. Ari and a friend want a fair way to pick who reads first, using three fair coins. Which rule is fair?
- 0 or 1 heads picks Ari; 2 or 3 heads picks the friend
- All three coins match picks Ari; anything else picks the friend
- 3 heads picks Ari; anything else picks the friend
8.
Number cube 1–6; coins HH, HT, TH, TT. Bo and two friends want a fair way to pick who clears the art table each week. Which rule is fair?
- Two fair coins: two heads, two tails or one of each picks each person
- A fair number cube: 1–2, 3–4 or 5–6 picks each person
- A fair number cube: 1, 2–3 or 4–6 picks each person
9.
The 36 cells of two number cubes. Esme and a friend want a fair way to pick who chooses the class song, using two fair number cubes. Which rule is fair?
- Both cubes the same picks Esme; different picks the friend
- A sum of 7 or less picks Esme; 8 or more picks the friend
- An even sum picks Esme; an odd sum picks the friend
10.
Spinner red, red, red, blue, green; number cube 1–6. Jun and a friend want a fair way to pick who feeds the class fish. A spinner has 5 equal sections: red, red, red, blue and green. Which rule is fair?
- A fair number cube: 1–3 picks Jun; 4–6 picks the friend
- The spinner: red or blue picks Jun; green picks the friend
- The spinner: red picks Jun; blue or green picks the friend

11th grade Games of chance: expected payoff, the better bet and fair decisions worksheet – printable — Print: 1 2 3 4 5 6

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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