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 = $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
4. 4.

   $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: its plain average is $500, against $450
   • The fair: it can earn $900
   • The bake sale: expected earnings $450, against $420
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?

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

   $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
   • They are the same: each has expected cost of $200
   • Plan A: its plain average is $200, against $366.67
   • Plan B: expected cost $170, against $200
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 a chance of 21/36 = 7/12
   • Fair: each has a chance of 1/2
   • Not fair: Ari has 6 of the 11 sums, a chance of 6/11
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 6 of the 11 sums, a chance of 6/11
   • Fair: each has a chance of 18/36 = 1/2
   • Not fair: Bo has a chance of 21/36
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.

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