Games of chance: expected payoff, the better bet and fair decisions
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
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?
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?
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?
Read this first
Equally likely outcomes
HH, HT, TH, TT.
Noah and a friend toss two fair coins. If the coins match, Noah goes first; if not, the friend does. Is the rule fair?
- Not fair: matching has a chance of 2/3
- Fair: each has a chance of 1/2
- Not fair: matching has a chance of 1/4
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
- Not fair: one of each has a chance of 1/2
- Fair: each has a chance of 1/4
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
- Fair: there are two groups, so each has a chance of 1/2
- Not fair: Ren has a chance of 2/3
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?
- Fair: red or not red, so each has a chance of 1/2
- Not fair: Tala has a chance of 3/4
- Not fair: the friend has a chance of 3/4
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.
A factory manager shows Bo the costs of fixing one batch of parts and their chances. What is the expected fixing cost per batch?
Use this
Table: no repair, flat tire, new wheel; cost = $0, $30, $90; chance = 0.6, 0.3, 0.1; cost × chance = $0, $9, $9.
A bike shop owner shows Esme a month of repair costs for one rental bike. What is the expected repair cost for the month?
Table
No repair, new keys, new screen, new laptop; cost = $0, $80, $250, $600; chance = 0.7, 0.2, 0.08, 0.02; cost × chance = $0, $16, $20, $12. Dot plot: number line $0 to $600, each stack as tall as its chance.
The school office shows Jun a year of repair costs for one class laptop. What is the expected repair cost for the year?