A charity is raising money by selling two thousand raffle tickets for $2 each. There is one grand prize worth $500, three secondary prizes worth $200 each, and eight third level prizes worth $20 each.
a) P(Win $200)
[Select]
b) P(Lose $2)
[ Select ]
c) What is the expected value of $2 raffle ticket?
[ Select ]
d) How much does the charity expect to make on the raffle?
well, there are 2012 total prizes. so,
(a) 3/2012
(b) 2000/2012
see what you can do on (c) and (d)
a) P(Win $200):
To calculate the probability of winning $200, we need to determine the number of ways to win $200 and divide it by the total number of possible outcomes.
Number of ways to win $200: 3 (since there are three secondary prizes worth $200 each)
Total number of possible outcomes: 2000 (since there are 2000 raffle tickets)
Probability of winning $200 = Number of ways to win $200 / Total number of possible outcomes
= 3 / 2000
b) P(Lose $2):
To calculate the probability of losing $2, we need to determine the number of losing outcomes (i.e., not winning any prize) and divide it by the total number of possible outcomes.
Number of losing outcomes = Total number of possible outcomes - Number of winning outcomes
Number of winning outcomes = Number of grand prizes + Number of secondary prizes + Number of third level prizes
= 1 + 3 + 8
= 12
Number of losing outcomes = Total number of possible outcomes - Number of winning outcomes
= 2000 - 12
Probability of losing $2 = Number of losing outcomes / Total number of possible outcomes
= (2000 - 12) / 2000
c) Expected value of $2 raffle ticket:
To calculate the expected value, we need to multiply each possible outcome (prize value) by its corresponding probability and sum them up.
Expected value = (Prize value 1 * Probability of winning Prize 1) + (Prize value 2 * Probability of winning Prize 2) + ...
Expected value = ($500 * P(Grand Prize)) + ($200 * P(Secondary Prize)) + ($20 * P(Third Level Prize)) + (-$2 * P(Lose $2))
d) To calculate how much the charity expects to make on the raffle, we need to multiply the number of raffle tickets sold by the price of each ticket.
Expected proceeds = Number of raffle tickets sold * Price per ticket
a) To find the probability of winning $200, we need to determine how many chances there are to win $200 and divide it by the total number of possible outcomes. In this case, there are 3 secondary prizes worth $200 each, so the number of chances to win $200 is 3. The total number of tickets sold is 2000. Therefore, the probability of winning $200 is 3/2000.
b) To find the probability of losing $2, we need to determine how many tickets result in losing and divide it by the total number of possible outcomes. In this case, every ticket has a chance of losing $2. So, the number of tickets that result in losing is 2000. The total number of tickets sold is also 2000. Therefore, the probability of losing $2 is 2000/2000, which is 1.
c) The expected value of a $2 raffle ticket is the sum of the products of each possible outcome and its probability. In this case, the possible outcomes are winning $500, winning $200, winning $20, and losing $2. The corresponding probabilities are 1/2000, 3/2000, 8/2000, and 2000/2000, respectively. So, the expected value can be calculated as follows:
Expected value = (500 * 1/2000) + (200 * 3/2000) + (20 * 8/2000) + (-2 * 2000/2000)
d) To calculate how much the charity expects to make on the raffle, we need to subtract the expenses from the total revenue. The total revenue can be found by multiplying the number of tickets sold (2000) by the price per ticket ($2). The expenses are the total value of the prizes (500 + 3*200 + 8*20). Therefore, the expected profit can be calculated as follows:
Expected profit = (2000 * $2) - (500 + 3*200 + 8*20)