Provide an appropriate response.

A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $8000 with a probability of 0.3. What is the expected profit?

To calculate the expected profit, we use the formula for **expected value**:

\[
\text{Expected Value} = (\text{Profit} \times \text{Probability of Profit}) + (\text{Loss} \times \text{Probability of Loss})
\]

In this case:
- Profit = $26,000, Probability of Profit = 0.7
- Loss = -$8,000, Probability of Loss = 0.3

Substituting the values:

\[
\text{Expected Profit} = (26,000 \times 0.7) + (-8,000 \times 0.3)
\]
\[
\text{Expected Profit} = 18,200 - 2,400 = 15,800
\]

So, the expected profit is **$15,800**.

Would you like a detailed explanation of how expected value works or have any other questions?

Here are five related questions:
1. How would the expected profit change if the loss was $10,000 instead of $8,000?
2. What happens to the expected profit if the probability of the profit decreases to 0.6?
3. Can you calculate the variance of the profit and loss outcomes?
4. What is the importance of expected value in business decision-making?
5. How does risk (like weather or strikes) affect expected value?

**Tip:** Always account for probabilities adding up to 1 when calculating expected values!

A contractor is considering a sale that promises a profit of $26,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $8000 with a probability of 0.3. What is the expected profit?

Discover how to calculate the expected profit in a business scenario where a contractor faces either a profit of $26,000 with a probability of 0.7 or a loss of $8,000 with a probability of 0.3. The solution involves applying the expected value formula, a key concept in probability and decision-making under uncertainty. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation