Question

For a multistate​ lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete part A.

A. If the grand prize is $15,000,000​, find and interpret the expected cash prize. If a ticket costs​ $1, what is your expected profit from one​ ticket?

The expected cash prize is $ ________

B. To the nearest​ million, how much should the grand prize be so that you can expect a​ profit? Assume nobody else wins so that you do not have to share the grand prize.

C. Does the size of the grand prize affect your chance of​ winning? Explain.

Table is below:

x (Cash prize)	P(x)
Grand prize	.0.00000000617
200,000	0.00000037
10,000	0.000001745
100	0.000138611
7	0.004471829
4	0.008147354
3	0.01353382
0	0.97370626483

Answer 1

y=c(0.00000000617,0.00000037,0.000001745,0.000138611,0.004471829,0.008147354,0.01353382,0.97370626483)
> sum(y)
[1] 1

x=c(15000000,200000,10000,100,7,4,3,0)
> x

a)

t=x*y
> t
[1] 0.09255000 0.07400000 0.01745000 0.01386110 0.03130280 0.03258942 0.04060146 0.00000000
> sum(t)
[1] 0.3023548

b)

> y=y[-c(1)]
> y
[1] 0.000000370 0.000001745 0.000138611 0.004471829 0.008147354 0.013533820 0.973706265
> x=x[-c(1)]
> x
[1] 2e+05 1e+04 1e+02 7e+00 4e+00 3e+00 0e+00
> y*x
[1] 0.07400000 0.01745000 0.01386110 0.03130280 0.03258942 0.04060146 0.00000000
> sum(y*x)
[1] 0.2098048
> (1-sum(y*x))/0.00000000617
[1] 128070538

THe price should be  128070538 =128 Millons(approx)

c)

it affects very less basically it affect nill

because the prob of winning is less =1-0.97370626483=0.027(aprrox)