question archive For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities
For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities
Subject:StatisticsPrice:2.87 Bought7
For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts (a) through (c) below
k(cash prize. $ ) Grand prize 200,000 10,000 100 7 4 3 0
P(x) 0.00000000764 0.00000019 0.000001787 0.000143787 0.004859191 0.006351519 0.01781606 0.97082745836
(a) If the grand prize is $13,000,000, 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 SRound to the nearest cent as needed.) What is the correct interpretation of the expected cash prize?
A. You will win $0.28 on every lottery ticket. On average,
B. you will win $0.28 per lottery ticket. On average,
C. you will profit $0.28 per lottery ticket.
The expected profit from one $1 ticket 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.
A. No, because the expected profit is always $0 no matter what the grand prize is.
B. No because vour chance of winninn is determined by the properties of the Iottery not the payouts.
C. Yes, your expected profit increases as the profit prize increases.
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
Answer:
a)
| x | P(X) | x*P(X) |
| 13000000 | 0.00000001 | 0.09932000 |
| 200000 | 0.00000019 | 0.03800000 |
| 10000 | 0.00000179 | 0.01787000 |
| 100 | 0.00014379 | 0.01437870 |
| 7 | 0.00485919 | 0.03401434 |
| 4 | 0.00635152 | 0.02540608 |
| 3 | 0.01781606 | 0.05344818 |
| 0 | 0.97082746 | 0.00000000 |
| total= | 1 | 0.282437293 |
so, expected cash prize is =$0.28
on average ,you win $0.28 per ticket.
If a ticket costs $1, the expected profit = 0.28 - 1 = - $ 0.72
b)
Let the grand prize be donoted by G. To expect a profit, we should have ∑x*P(x) -1 > 0
| x | P(X) | x*P(X) |
| G | 0.00000001 | G*0.00000001 |
| 200000 | 0.00000019 | 0.03800000 |
| 10000 | 0.00000179 | 0.01787000 |
| 100 | 0.00014379 | 0.01437870 |
| 7 | 0.00485919 | 0.03401434 |
| 4 | 0.00635152 | 0.02540608 |
| 3 | 0.01781606 | 0.05344818 |
| 0 | 0.97082746 | 0.00000000 |
| total= | 1 | G*0.00000001+0.183117 |
so,
G*0.00000001+0.183117-1>0
G*0.00000001>0.813883
G>0.813883/0.00000001
| G>106921820.3 |
so,G=approx 107M
c)
The Grand prize doesn't affect the chances of winning, because the probability distribution is fixed, but it affects the chances of winning a profit, because a large grand prize, even with a small probability of winning the grand prize, will affect the expected winnings from the lottery. A large grand prize will lead to a higher expected profit from the lottery and vice versa.
so, option b) is answer.
