We are given a total of 3,000,000 people buy lottery tickets for this game and each ticket costs $20. The layout for the prizes is as follows:
Prize | # Winners
20 | 522,000
40 | 261,000
50 | 195,000
500 | 4,000
10,000 | 300
1,000,000 | 3
- Calculate the the pmf of p = amount of prize for random ticket
- If I purchase one ticket what is my expected gain?
- If I pay an extra $10 my prize is multiplied by 2. What is my expected gain if buy a ticket and pay an extra 10?
Solution: This is what I have so far
For the pmf I have p(20) = 522,000/3,000,000 = .174 p(40) = 261,000/3,000,000 = .087 p(50) = .065 p(500) = .00133 p(10,000) = .0001 p(1,000,000)=.000001
To calculate expected gain I know i have to add up the probabilities of winning each of the prizes less the cost. So the expected gain of the $20 prize would be 0(.174) because the cost of the ticket is 20 and so on... thus the expected gain would be:
= 0(.174)+20(.087)+30(.065)+480(.00133)+9980(.0001)+999980(.000001) Is that correct?
The question continues to ask:
Suppose that I continue to buy tickets until I win a prize (of any amount). After I win a prize, I will not buy any more tickets. Let T be the number of tickets that I will buy.
- Find the pmf of T if the tickets are not independent of each other
- Under the assumption of independence, what is the distribution of T? Write the pmf. How many tickets would I expect to buy?
Any suggestions for these last two questions?