In a local lottery, there is a 15% chance of winning $1, a 5% chance of winning $5, a 1 in 100 chance of winning $50 and a 1 in 10 000 chance of winning $500.
What is the expected value of your winnings in this lottery?
How much does the lottery need to charge for each ticket to make a profit of 40% on each ticket sold.
Having trouble on even getting started here, could you give me a push in the right direction?
expected wins:
.15(1) = .15
.05(5) = .25
.01(50) = .50
1/10000(500) = .05
total expected wins on one ticket = .95
That is, if they charged 95 cents for a ticket , everybody would break even in the long run.
So to make a 40% profit, they should charge
.95(1.4) or $ 1.33
Sure! To calculate the expected value of your winnings in the lottery, you need to multiply each possible outcome by its respective probability, and then sum up the results.
For example, the calculation would look like this:
Expected value = (15% of $1) + (5% of $5) + (1 in 100 chance of $50) + (1 in 10,000 chance of $500)
To calculate the expected value, you need to convert the percentages to decimal form. So, 15% is equivalent to 0.15, 5% is equivalent to 0.05, and so on.
Let's do the calculations step by step:
Expected value = (0.15 * $1) + (0.05 * $5) + (1/100 * $50) + (1/10,000 * $500)
Expected value = $0.15 + $0.25 + $0.50 + $0.05
Expected value = $0.95
So, the expected value of your winnings in this lottery is $0.95. This means that, on average, you can expect to win $0.95 per ticket you buy.
Now let's move to the second question about the price the lottery needs to charge for each ticket to make a 40% profit on each ticket sold.
To answer this question, we need to determine the revenue the lottery will get from selling one ticket and compare it to its costs.
Let's assume the cost of producing a single lottery ticket is $C, and we want to make a profit of 40% on each ticket sold.
Revenue per ticket sold = Ticket price - Cost per ticket
Profit per ticket sold = Revenue per ticket sold - Cost per ticket
Profit per ticket sold = 40% of Ticket price - $C
Since we want to make a 40% profit, the equation can be written as:
40% of Ticket price = $C
To find the ticket price, we can rearrange the equation:
Ticket price = $C / 0.4
So, the lottery needs to charge a price equal to the cost per ticket divided by 0.4 (or 40%) to make a 40% profit on each ticket sold.
I hope this helps you get started! Let me know if you have any further questions.