A certain game involves tossing 3 fair coins, and it pays 14cents¢ for 3 heads,

Question

A certain game involves tossing 3 fair coins, and it pays 14cents¢ for 3 heads, 5cents¢ for 2 heads, and

3cents¢ for 1 head. Is 5cents¢ a fair price to pay to play this game? That is, does the 5cents¢

cost to play make the game fair?

A used-car dealer gets complaints about his cars as shown in the table.

Number of complaints per day

0

1

2

3

4

5

6

Probability

0.010.01

0.070.07

0.20.2

0.260.26

0.260.26

0.140.14

0.060.06

Find the expected number of complaints per day.

A college foundation raises funds by selling 600 raffle tickets for a new car worth

$44,000 at $100 each.

(a) Find the expected net winnings of a person buying one of the tickets.

(b) Find the total profit for the foundation, assuming they had to purchase the car.

(c) Find the total profit for the foundation, assuming the car was donated.

Twenty thousand raffle tickets are sold. One first prize of $3000, two second prizes of

$1000, and three third prizes of $200each will be awarded, with all winners selected randomly. If you purchased one ticket, what are your expected gross winnings?

A study at an amusement park found that, of10,000 families at the park, 1740 had brought one child,

2140 had brought two children, 2380 had brought three children, 1440 had brought four children, 1050 had brought fivechildren, 800 had brought six children, and 450 had not brought any children.

Find the expected number of children per family at the amusement park.

Number of complaints per day

0

1

2

3

4

5

6

Probability

0.010.01

0.070.07

0.20.2

0.260.26

0.260.26

0.140.14

0.060.06

Explanation / Answer

1Solution:-

2 solution:- E(x) = xp(x)

= (0*0.01)+(1*0.07)+(2*0.2)+(3*0.26)+(4*0.26)+(5*0.14)+(6*0.06)

= 3.35

3 solution:-

a)  

cost price = 600*100 = 60000

net winning = 44000 - 60000 = -16000

= Expected net winning = -16000/600 = -26.6666 = -27

b)  the total profit asuming they had purchase the car is  16000

c) the total profit asuming they had to donate the car is 60000

4 solution:-

(1/20000)*(3000) + (2/20000)*(1000) + (3/20000)*(200) + (7994/20000)*(0) = 0.28

5 solution:- (1/10000)*(1740)+(2/10000)*(2140)+(3/10000)*(2380)+(4/10000)*(1440)+(5/10000)*(1050)+(6/10000)*(800) + 0 = 2.897

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