A lottery has one $1000000 prize, two $50000 prizes, ten $1000 prizes, and two hundred $50 prizes. There are to be one milllion tickets sold. How much pofit does the lotto company make if they sell the tickets for $2.00 each?

P(x) of 1000000 is 1/1000000

P(x) of 50000 prize is 2/1000000
P(x) of 1000 prize ia 10/1000000
P(x) of 50 prize is 200/1000000

P(x)=p

Find E(x) for each one

E(x)= n.p

Then add all E(x) values to find the expected value of all prizes for one ticket

Finally, that that total and multiply it by the cost of the ticket which is 2 dollars.

This will give you the expected profit

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Oh also n is the total number of tickets which in this case is 1000000

To calculate the profit, we first need to determine the total revenue generated from selling the tickets.

Total revenue = Number of tickets sold * Price per ticket

Given that one million tickets are sold at a price of $2.00 each, the total revenue can be calculated as follows:

Total revenue = 1,000,000 tickets * $2.00 per ticket
Total revenue = $2,000,000

Now, let's calculate the total prize money that needs to be paid out.

Prize money = (Number of $1,000,000 prizes * $1,000,000) + (Number of $50,000 prizes * $50,000) + (Number of $1,000 prizes * $1,000) + (Number of $50 prizes * $50)

Prize money = (1 * $1,000,000) + (2 * $50,000) + (10 * $1,000) + (200 * $50)
Prize money = $1,000,000 + $100,000 + $10,000 + $10,000
Prize money = $1,120,000

Finally, to calculate the profit, we subtract the prize money from the total revenue.

Profit = Total revenue - Prize money
Profit = $2,000,000 - $1,120,000
Profit = $880,000

Therefore, the lotto company makes a profit of $880,000 if they sell the tickets for $2.00 each.

To find the profit that the lottery company makes, we need to calculate the total revenue from ticket sales and then subtract the total prize amount.

Step 1: Calculate the revenue from ticket sales
The price of each ticket is $2.00, and the total number of tickets sold is 1 million. So, the total revenue from ticket sales can be found by multiplying the ticket price by the number of tickets sold:
Total Revenue = Ticket Price × Number of Tickets Sold
Total Revenue = $2.00 × 1,000,000
Total Revenue = $2,000,000

Step 2: Calculate the total prize amount
To find the total prize amount, we need to calculate the sum of prizes for each prize category:
Total Prize Amount = ($1,000,000 Prize + $50,000 Prize + $50,000 Prize + $1,000 Prize + $1,000 Prize + ... + $50 Prize + $50 Prize)
Total Prize Amount = ($1,000,000 + $50,000 + $50,000 + $1,000 + $1,000 + ... + $50 + $50)
Total Prize Amount = $1,000,000 + 2 × $50,000 + 10 × $1,000 + 200 × $50
Total Prize Amount = $1,000,000 + $100,000 + $10,000 + $10,000
Total Prize Amount = $1,120,000

Step 3: Calculate the profit
The profit is obtained by subtracting the total prize amount from the total revenue from ticket sales:
Profit = Total Revenue - Total Prize Amount
Profit = $2,000,000 - $1,120,000
Profit = $880,000

Therefore, the lottery company makes a profit of $880,000 if they sell the tickets for $2.00 each.