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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   $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?

   0.6
2. 2.

   $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?

   0.25
3. 3.

   $600 if the machine jams, $100 if not. Old method: $300 for sure. Milo compares a factory's new method with its old one. What chance of a jam makes the two expected costs equal?

   0.4
4. 4.

   A factory makes 200 parts at $2 each. A passing part (chance 0.9) sells for $6; a failing part is recycled for $1. What expected profit for the batch does Pia find?

   $700
5. 5.

   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?

   $360
6. 6.

   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?

   $1,320
7. 7.

   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?

   $324
8. 8.

   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?

   • All three coins match picks Ari; anything else picks the friend
   • 3 heads picks Ari; anything else picks the friend
   • 0 or 1 heads picks Ari; 2 or 3 heads picks the friend
9. 9.

   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?

   • A fair number cube: 1, 2–3 or 4–6 picks each person
   • 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
10. 10.

    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?

    • An even sum picks Esme; an odd sum picks the friend
    • A sum of 7 or less picks Esme; 8 or more picks the friend
    • Both cubes the same picks Esme; different picks the friend