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

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   At the school fair's free ring toss, each throw gets a prize with chance 0.15. If 240 children each throw once, how many prizes should Jun expect to hand out?

   36
2. 2.

   A factory check finds that each bottle has a 0.02 chance of a loose cap. How many of 1,500 bottles should Kira expect to have a loose cap?

   30
3. 3.

   At a free bean-bag toss, each throw has a 0.35 chance of landing in the basket. How many of 160 throws should Luz expect to land in the basket?

   56
4. 4.

   In a drop test, each phone case has a 0.04 chance of cracking. How many of 2,500 cases should Milo expect to crack?

   100

5. Read this first

   Equally likely outcomes

   HH, HT, TH, TT.

6. 5.

   Noah and a friend toss two fair coins. If the coins match, Noah goes first; if not, the friend does. Is the rule fair?

   • Fair: each has a chance of 1/2
   • Not fair: matching has a chance of 2/3
   • Not fair: matching has a chance of 1/4
7. 6.

   Pia and two friends toss two fair coins: two heads picks Pia, two tails picks one friend, and one of each picks the other. Is the rule fair?

   • Fair: each has a chance of 1/3
   • Fair: each has a chance of 1/4
   • Not fair: one of each has a chance of 1/2
8. 7.

   1, 2, 3, 4, 5, 6. Ren and a friend roll a fair number cube. A 1 or 2 means Ren goes first; 3, 4, 5 or 6 means the friend does. Is the rule fair?

   • Not fair: the friend has a chance of 2/3
   • Not fair: Ren has a chance of 2/3
   • Fair: there are two groups, so each has a chance of 1/2
9. 8.

   Red, blue, yellow, green. Tala and a friend spin a spinner with 4 equal sections: red, blue, yellow and green. Red means Tala goes first; any other color means the friend does. Is the rule fair?

   • Not fair: Tala has a chance of 3/4
   • Fair: red or not red, so each has a chance of 1/2
   • Not fair: the friend has a chance of 3/4

10. Use this

    Table: no repair, screen fix, new phone; cost = $0, $120, $400; chance = 0.75, 0.2, 0.05; cost × chance = $0, $24, $20.

11. 9.

    Zee's teacher lists a year of phone repair costs and their chances. What is the expected repair cost for the year?

    $44

12. Use this

    Table: no fix, small fix, big fix; cost = $0, $50, $300; chance = 0.7, 0.25, 0.05; cost × chance = $0, $12.50, $15.

13. 10.

    A factory manager shows Bo the costs of fixing one batch of parts and their chances. What is the expected fixing cost per batch?

    $27.50