I only need my answer to be checked.
In a lottery, 5,000 tickets are sold for $1. One first place prize of $1,000, 1 second prize of $500, 4 third prizes of $100 and 10 consolation prizes of $10. What is the expected net earnings of a person who buys a ticket?
(1000) (1/5000) + (500) (1/5000) + (10) (10,5000)
= .2+.1+.02=.32
Sold for $1: 1- .32 =.68
What happened to the 4 of 100 each?
what is (10) (10,5000)
maybe (10) (10/5000)
by the way, my expected earnings are negative :)
anyway they give out
1000 + 500 + 400 + 100 = 2000
so per ticket that is 2000/5000 = 0.40
or 40 cents each
expect to lose 60 cents of your dollar
total expected earnings for the sponsor = 5000-2000 = 3000
so the sponsor makes that 60 cents per dollar
To check your answer, we can calculate the expected net earnings directly using the given information.
There are a total of 5,000 tickets sold for $1 each. So, the total amount collected from ticket sales is 5,000 * $1 = $5,000.
Now, let's calculate the expected net earnings step-by-step:
1. First place prize: The probability of winning the first prize is 1 out of 5,000 tickets. The amount won is $1,000. So, the expected value for the first place prize is (1/5,000) * $1,000 = $0.2.
2. Second place prize: The probability of winning the second prize is 1 out of 5,000 tickets. The amount won is $500. So, the expected value for the second place prize is (1/5,000) * $500 = $0.1.
3. Third place prizes: There are 4 third place prizes, and each one has a probability of 1 out of 5,000 tickets. The amount won for each third place prize is $100. So, the total expected value for the third place prizes is 4 * (1/5,000) * $100 = $0.08.
4. Consolation prizes: There are 10 consolation prizes, and each one has a probability of 1 out of 5,000 tickets. The amount won for each consolation prize is $10. So, the total expected value for the consolation prizes is 10 * (1/5,000) * $10 = $0.02.
Now, let's sum up all the expected values:
$0.2 + $0.1 + $0.08 + $0.02 = $0.4.
Therefore, the expected net earnings of a person who buys a ticket is $0.4.
As you can see, your calculated answer of $0.32 is slightly lower than the correct answer of $0.4. It seems like you missed including the expected value for the third place and consolation prizes in your calculation.