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Solved: Powerball Powerball is a multistate lottery. The
Chapter 11, Problem 33AYU(choose chapter or problem)
Powerball is a multistate lottery. The following probability distribution represents the cash prizes of Powerball with their corresponding probabilities.
x(cash prize, $) |
P(x) |
Grand prize |
0.00000000684 |
200,000 |
0.00000028 |
10,000 |
0.000001711 |
100 |
0.000153996 |
7 |
0.004778961 |
4 |
0.007881463 |
3 |
0.01450116 |
0 |
0.9726824222 |
(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?
(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.
Questions & Answers
QUESTION:
Powerball is a multistate lottery. The following probability distribution represents the cash prizes of Powerball with their corresponding probabilities.
x(cash prize, $) |
P(x) |
Grand prize |
0.00000000684 |
200,000 |
0.00000028 |
10,000 |
0.000001711 |
100 |
0.000153996 |
7 |
0.004778961 |
4 |
0.007881463 |
3 |
0.01450116 |
0 |
0.9726824222 |
(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?
(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.
ANSWER:
Step 1 of 3
The following probability distribution represents the cash prizes of Powerball with their corresponding probabilities.
|
x(cash prize, $) |
P(x) |
|
Grand prize |
0.00000000684 |
|
200,000 |
0.00000028 |
|
10,000 |
0.000001711 |
|
100 |
0.000153996 |
|
7 |
0.004778961 |
|
4 |
0.007881463 |
|
3 |
0.01450116 |
|
0 |
0.9726824222 |