A contractor is considering a sale that promises a profit of $20,000 with a probability of .7 or a loss ( due to bad weather, strikes, and such) of $3000 with a probability of .3. What is the expected profit?
a. 13,100
b. 17,000
c. 14,000
d. 16,100
expected value of profit= .7*20,000 -.3*3000
To calculate the expected profit, we multiply each possible profit outcome by its associated probability and sum them up.
In this case, there are two possible outcomes: a profit of $20,000 with a probability of 0.7, and a loss of $3,000 with a probability of 0.3.
To calculate the expected profit, we can use the following formula:
Expected profit = (Profit 1 * Probability 1) + (Profit 2 * Probability 2) + ...
Let's calculate it step by step:
Profit 1 = $20,000
Probability 1 = 0.7
Profit 2 = -$3,000 (since it represents a loss)
Probability 2 = 0.3
Expected profit = ($20,000 * 0.7) + (-$3,000 * 0.3)
Multiplying each profit by its probability:
Expected profit = $14,000 + (-$900)
Adding up the results:
Expected profit = $13,100
Therefore, the expected profit is $13,100.
Hence, the correct option is a. 13,100.