a contractor is considering a sale that promises a profit of $20,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $10,000 with a probability of 0.3. What is the expected profit?
To calculate the expected profit, we need to take into account the probabilities of each outcome and their corresponding profits.
Let's denote the profit of $20,000 with the probability of 0.7 as P1, and the loss of $10,000 with the probability of 0.3 as P2.
The expected profit, denoted as E(P), is calculated as:
E(P) = P1 * Profit1 + P2 * Profit2
E(P) = 0.7 * $20,000 + 0.3 * (-$10,000)
E(P) = $14,000 - $3,000
E(P) = $11,000
Therefore, the expected profit is $11,000.