A contractor is considering a sale that promises a profit of \( \$ 24,000 \) with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of \( \$ 2000 \) with a probability of 0.3 . What is the expected profit? O \( \$ 22,000 \) \( \$ 16,800 \) o \( \$ 18,200 \) \$ \( \$ 16,200 \) \$ \( \$ 14,400 \)

To calculate the expected profit, you can use the formula for expected value, which involves multiplying the value of each outcome by its probability and then summing them up. Here, you have two scenarios: 1. Profit of \( \$ 24,000 \) with a probability of 0.7: \( 24,000 \times 0.7 = 16,800 \) 2. Loss of \( \$ 2,000 \) with a probability of 0.3: \( -2,000 \times 0.3 = -600 \) Now, sum these values: \[ 16,800 - 600 = 16,200 \] So, the expected profit is \( \$ 16,200 \). Now that you've got your answer, let’s clarify it with some additional context! Did you know that the concept of expected value has its roots in decision-making under uncertainty, dating back to the 18th century? Mathematicians like Daniel Bernoulli started formalizing it to help people make better choices when faced with risky outcomes, giving rise to modern probability theory! In real life, understanding expected profit can greatly aid contractors in making informed business decisions. By calculating expected values for various projects, contractors can prioritize jobs that offer the best risk-adjusted returns, ensuring smarter resource allocation and enhanced profitability over time!