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

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Amount = $0, $30, $100; chance = 0.75, 0.2, 0.05. Kira's coach pays $60 a year for a phone plan. With it, a screen fix costs $30 (chance 0.2) and a new phone $100 (chance 0.05). What is the coach's expected yearly cost?

   $71
2. 2.

   Amount = $400, $100; chance = 0.7, 0.3. A club's car wash earns $400 on a dry day (chance 0.7) or $100 on a rainy day. Supplies cost $50. What are Luz's club's expected earnings after supplies?

   $260
3. 3.

   Amount = $6, $1; chance = 0.9, 0.1. Each part costs a factory $2 to make. It sells for $6 if it passes the check (chance 0.9), or is recycled for $1. What expected profit per part does Milo find?

   $3.50
4. 4.

   Amount = $300, $180, $60; chance = 0.6, 0.3, 0.1. A club's bake sale earns $300 if sunny (chance 0.6), $180 if cloudy (chance 0.3) or $60 if rainy. The table costs $40. What are Noah's club's expected earnings after the table?

   $200
5. 5.

   $60 (chance 1). Plan B: $0 (chance 0.85), $100 (chance 0.1), $500 (chance 0.05). Ren's teacher compares two phone plans for a year. Plan A costs $60 and covers all repairs; Plan B has no fee but pays for repairs. Which plan has the lower expected cost?

   • They are the same: each has expected cost of $60
   • Plan A: its plain average is $60, against $200
   • Plan A: the other plan could cost $500
   • Plan B: expected cost $35, against $60
6. 6.

   $600 (chance 0.7), $0 (chance 0.3). The book sale: $500 (chance 0.5), $300 (chance 0.5). Tala's club can run a car wash or a book sale. The table gives the earnings and their chances. Which choice has the greater expected earnings?

   • The book sale: its plain average is $400, against $300
   • The car wash: expected earnings $420, against $400
   • They are the same: each has expected earnings of $400
8. 7.

   Ari and a friend roll two fair number cubes and add them. Ari goes first on a sum of 7 or less, and the friend on 8 or more. Is the rule fair?

   • Not fair: Ari has 6 of the 11 sums, a chance of 6/11
   • Fair: each has a chance of 1/2
   • Not fair: Ari has a chance of 21/36 = 7/12
9. 8.

   Bo and a friend roll two fair number cubes and add them. Bo goes first on an even sum, and the friend on an odd sum. Is the rule fair?

   Use the picture in question 7.

   • Not fair: Bo has a chance of 21/36
   • Not fair: Bo has 6 of the 11 sums, a chance of 6/11
   • Fair: each has a chance of 18/36 = 1/2
10. 9.

    Esme and a friend roll two fair number cubes and add them. Esme goes first on a sum of 6, 7 or 8, and the friend on any other sum. Is the rule fair?

    Use the picture in question 7.

    • Not fair: Esme has 3 of the 11 sums, a chance of 3/11
    • Fair: each has a chance of 1/2
    • Not fair: the friend has a chance of 20/36 = 5/9
11. 10.

    Jun and a friend roll two fair number cubes and add them. Jun goes first on a sum of 2 to 6 or 10, and the friend on any other sum. Is the rule fair?

    Use the picture in question 7.

    • Fair: each has a chance of 18/36 = 1/2
    • Not fair: Jun has a chance of 21/36
    • Not fair: Jun has 6 of the 11 sums, a chance of 6/11