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 |
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)
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