# Win a $10 or$5 Prize in Tom's 4/19 Lottery Fundraiser

• MHB
• heyhey11
In summary: For (c), without knowing how much it costs to print a ticket, it is impossible to say what the expected profit on 100 tickets would be. In summary, the conversation discusses a lottery fundraiser where 4 winning numbers will be randomly selected out of a set of 19 numbers. There are different prizes for matching different numbers, and the questions involve determining the chance of winning certain prizes, the appropriate cost per ticket, and the expected profit on a set number of tickets. The first question is solved using probability calculations, but the second and third questions require more information about the cost and expected revenue of the fundraiser.
heyhey11
hello! I have two questions I needed some help with.

2. Tom is having a 4/19 lottery as a fundraiser; 4 winning numbers will be randomly selected without replacement out of the numbers from 1 to 19 inclusive. (similar to Ontario’s 6/49, with smaller numbers) The prizes are described below. For the questions below, define an appropriate random variable X.
Tickets Prize
All 4 winning numbers 1000 dollars
Any 3 of the winning numbers 100
Any 2 of the winning numbers 10
Any 1 of the winning numbers 5
None of the winning numbers 0
a) Tom claims that there is over a 60% chance that you can win a $10 or$5 prize. Is his claim correct?
b) What would be an appropriate cost per ticket. Explain your answer.
c) Given the cost suggested in part b), what is his expected profit on 100 tickets?
Note: Order doesn't matter for the numbers

I solved part a and got
p(X=4)= 1/19C4= 1/3876
p(X=3)= (4C3 * 15C1)/3876= 60/3876
p(X=2)= (4C2 * 15C2)/3876= 630/3876
p(X=1)= (4C1 * 15C3)/3876= 1820/3876
a. (630 + 1820)/3876≈ 0.632. which is 63.2%, so yes his claim is correct.

I needed help with b and c. For b, I know I should calculate expectations and then choose a price that gives a good revenue based on payout but I wasn't sure how.

3. A discrete random variable, X, is uniformly distributed between 1 and 10 inclusive and another discrete random variable, Y, is uniformly distributed between 5 and 15 inclusive. If one number from each set is selected at random, then determine P(Y < X ) .

I solved it the following:
(15 cases in which Y < X) ÷ (110 possible pairs) = 3/22

I got 15 cases because if Y is 5, X can be 6-10 (5 options), then if Y is 6, X can be 7-10 (4 options), if Y is 7, X can be 8-10 (3 options), if Y is 8, X can be 9 or 10 (2 options) and if Y is 9, X can be 10 ( 1 option).
5 +4+3+2+1= 15 cases in which Y < X)
and 11 X values x 10 Y values = 110 possible pairs

But I feel like it's the wrong approach as it doesn't use any probability distribution formula so I was looking for some help on it too.

For (b), to determine how much should be charged for a ticket, you idea would be correct if this were to be a "break even" event- all money brought in going out as prizes. But it isn't, it is a "fund-raiser"! Without knowing how much money is expected to be raised, it is impossible to say how much should be charged per ticket.

## 1. How do I enter the lottery fundraiser?

To enter the lottery fundraiser, you can purchase a ticket from Tom or any designated sellers. The ticket will have a number on it, which will serve as your entry into the drawing.

## 2. How much does it cost to enter the lottery fundraiser?

The cost of a ticket for the lottery fundraiser is either $10 or$5, depending on the prize you choose to enter for. The $10 prize will have a higher value prize, while the$5 prize will have a lower value prize.

## 3. When is the drawing for the lottery fundraiser?

The drawing for the lottery fundraiser will take place on April 19th, as indicated in the title of the fundraiser. The exact time and location of the drawing will be announced closer to the date.

## 4. How will the winner be chosen for the lottery fundraiser?

The winner will be chosen through a random drawing of all the ticket numbers entered into the fundraiser. This ensures a fair and unbiased selection process.

## 5. What are the prizes for the lottery fundraiser?

The prizes for the lottery fundraiser are either a $10 or$5 prize, as indicated in the title. The specific prize for each category will be announced closer to the date of the drawing.

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