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.

   $900 (chance 0.4), $100 (chance 0.6). The bake sale: $450 (chance 1). Pia's club can hold an outdoor fair or an indoor bake sale. The table gives the earnings and their chances. Which choice has the greater expected earnings?

   • They are the same: each has expected earnings of $420
   • The fair: it can earn $900
   • The bake sale: expected earnings $450, against $420
   • The fair: its plain average is $500, against $450
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
   • They are the same: each has expected earnings of $400
   • The car wash: expected earnings $420, against $400
7. 7.

   $200 (chance 1). Plan B: $0 (chance 0.6), $300 (chance 0.3), $800 (chance 0.1). The school office compares two tablet plans for Zee's class for a year. Plan A costs $200; Plan B has no fee but pays for repairs. Which plan has the lower expected cost?

   • Plan A: the other plan could cost $800
   • Plan A: its plain average is $200, against $366.67
   • They are the same: each has expected cost of $200
   • Plan B: expected cost $170, against $200
9. 8.

   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?

   • Fair: each has a chance of 1/2
   • Not fair: Ari has a chance of 21/36 = 7/12
   • Not fair: Ari has 6 of the 11 sums, a chance of 6/11
10. 9.

    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 8.

    • Fair: each has a chance of 18/36 = 1/2
    • Not fair: Bo has 6 of the 11 sums, a chance of 6/11
    • Not fair: Bo has a chance of 21/36
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 8.

    • 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