At a fair run by a local charity organization, it costs 50 cents to try one’s luck in drawing an ace from a deck of 52 playing cards. What is the expected profit per customer, if they pay $4 if and only if a person draws an ace?
I answered the identical question for Carlos on Sat at 9:18, look about half way down this page
To calculate the expected profit per customer, we need to determine the probability of drawing an ace and the amount of profit made for each outcome.
First, let's find the probability of drawing an ace. In a standard deck of 52 playing cards, there are 4 aces. Therefore, the probability of drawing an ace is 4/52 or 1/13.
Next, let's calculate the profit for each outcome. If a person draws an ace, they pay $0.50 to play and win $4, resulting in a profit of $4 - $0.50 = $3.50. If a person does not draw an ace, they still pay $0.50 to play but do not win anything, resulting in a profit of -$0.50.
Now, we can calculate the expected profit using the probabilities and profits for each outcome. The expected profit is calculated by multiplying each profit by its respective probability and then summing them up.
Expected Profit = (Probability of drawing an ace * Profit for drawing an ace)
+ (Probability of not drawing an ace * Profit for not drawing an ace)
Expected Profit = (1/13 * $3.50) + (12/13 * -$0.50)
Expected Profit = ($3.50/13) - ($6/13)
Expected Profit = -$2.50/13
Therefore, the expected profit per customer for the charity organization is approximately -$0.1923. This means, on average, the charity organization is expected to lose approximately $0.1923 per customer.