Question

1. A raffle has a prize of $ 1000, two prizes of $ 500, five prizes of $ 100 and 50 prizes of $ 10. If 1000 tickets are sold and the raffle organizers intend to make a profit of $ 10 per ticket, how much must a ticket buyer pay?

2. In a betting game, a person earns $ 800 if by tossing three coins on the air all faces or all stamps are obtained and he pays $ 350 if one or two faces result. What is the expected gain for this person?

3. A factory that produces certain types of tires has the following information: 65% of the tires it produces are without defects, 15% with repairable defects and 20% with non-repairable defects. A tire without defects generates a net profit of $ 5000, one with repairable defects $ 2300 and one with non repairable defects generates a loss of $ 1200. If G is the utility per tire, calculate the expected value of G and its standard deviation.

**please answer all, thanks!! I appreciate it

Answer 1

1)

Let random variable, X=loss incurred by organizer.

The expected value for random variable, X is obtained using the formula,

loss,X	probability,P(X)	X*P(X)
-1000	1/1000=0.001	-1
-500	2/1000=0.002	-1
-100	5/1000=0.005	-0.5
-50	50/1000=0.05	-2.5
	Sum	-5

The expected loss per ticket = $5.

To get a profit of $10 per ticket, the organizer need to price a ticket of $15.

2)

Let X be the random variable of amount won.

Probability of winning $800 such that getting all the faces (all heads or all tails)

Now, the expected value is obtained using the formula,

X	probability,P(X)	X*P(X)
800	0.25	200
-350	0.75	-262.5
Sum		-62.5

3)

Let X be the random variable of amount of profit.

The expected value is obtained using the formula,

	probability,P(X)	X	X*P(X)
without defects	0.65	5000	3250
repairable defects	0.15	2300	345
non-repairable defects	0.2	-1200	-240
			3355