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 am sorry that nobody has responded to your post earlier.
The probability of geting an ace is 4/52. The probability of not getting an ace is 48/52. They will receive $.50 every time a person draws, but lose $4 4 times in 52. Thus, by chance, they will gain $26 and lose $16 over 52 customers. Dividing the different between these two amounts by the number of customers will give you the "expected profit per customer."
I hope this helps. Thanksfor asking.
To calculate the expected profit per customer, we need to first find the probability of drawing an ace and the probability of not drawing an ace.
The probability of drawing an ace is given as 4/52, since there are four aces in a deck of 52 cards.
The probability of not drawing an ace is calculated by subtracting the probability of drawing an ace from 1:
Probability of not drawing an ace = 1 - (4/52) = 48/52.
Now, let's calculate the expected profit per customer.
For every customer, they pay 50 cents to try their luck in drawing an ace. So, the revenue per customer is 0.50 dollars.
If a person draws an ace, the organization receives an additional $4 from that customer. This happens with a probability of 4/52.
The profit from each customer can be calculated by subtracting the cost (0.50 dollars) from the revenue (0.50 dollars + 4 dollars):
Profit per customer = (0.50 + 4) - 0.50 = 4 dollars.
Now, let's calculate the expected profit per customer. The expected profit is the average profit per customer over all possible outcomes.
The expected profit per customer can be calculated as follows:
Expected profit per customer = (profit per customer) * (probability of drawing an ace) + (0 dollars) * (probability of not drawing an ace)
Expected profit per customer = (4 * (4/52)) + (0 * (48/52))
Expected profit per customer = (16/52) + 0
Expected profit per customer = 16/52.
Simplifying the fraction, the expected profit per customer is approximately 0.3077 dollars.
Therefore, on average, the organization can expect to make a profit of approximately 30.77 cents per customer.