Question

According to the California Lottery, the odds of winning the PowerBall is 1 in 292,201,338. This week’s estimated prize is $0.6 billion and one ticket costs $2.

a. Calculate the Expected value and standard of deviation of playing the lottery.
b. Would a risk-neutral person play the lottery? Explain.

c. How about a risk-averse or risk neutral person? Explain.

Answer 1

Solution .
A.	Calculate the Expected value and standard of deviation of playing the lottery.
	The expected value, EV, of the lottery is equal to the sum of the returns weighted by their probabilities:
	EV= Prob.(Prize Amount)
	0.205338
	$0.205338 Billions
	Working Notes :-
probability	3.4223E-09
	Approx. 3.4223
Prize Amount	$0.6 billions
	Standard Deviation
	The variance, Ā2, is the sum of the squared deviations from the mean, $27, weighted by their probabilities:
	Ā2=(3.4223)(.06-0.205338)^2
	$0.0722897023232412 Billions
B.	A risk-neutral person would pay the expected value of the lottery: $.205338 billions
C.	Risk Neutral
	People with risk neutral preferences simply wants to maximize their expected value. The risk-neutral investor places himself in the middle of the risk spectrum, represented by risk-seeking investors at one end.
	Risk Averse
	People with risk averse preferences is willing to take an amount of money smaller than the expected value of a lottery.A risk averse investor avoids risks.In other words, among various investments giving the same return with different level of risks, this investor always prefers the alternative with least interest. investors want less risk and less return.