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.

   $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
2. 2.

   $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
3. 3.

   $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?

   0.2
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?

   • 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
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?

   • Two fair coins: two heads, two tails or one of each picks each person
   • A fair number cube: 1, 2–3 or 4–6 picks each person
   • A fair number cube: 1–2, 3–4 or 5–6 picks each person
10. 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?

    • The spinner: red or blue picks Jun; green picks the friend
    • A fair number cube: 1–3 picks Jun; 4–6 picks the friend
    • The spinner: red picks Jun; blue or green picks the friend