Short Answer 
The expected value is a statistical measure used to calculate the average outcome of a random variable using its probabilities. In this case, with a 75% probability of success yielding $44,000 and a 25% probability of failure resulting in a loss of $196,000, the expected value is calculated at -$16,000, indicating the project is likely to result in a loss and should not be pursued.
Step 1: Understanding Expected Value
The expected value of a discrete distribution is a statistical measure that calculates the average outcome of a random variable based on its probabilities. It is computed by summing up all possible outcomes, each multiplied by its corresponding probability. This allows businesses to assess the potential profitability or loss of a project by considering both gains and losses.
Step 2: Analyzing the Scenario
In this scenario, there are two possible outcomes for the new product: success or failure. The estimated probabilities and revenues are:
- Success: 75% probability with a revenue of $44,000.
- Failure: 25% probability with a revenue of -$196,000.
This sets up the distribution for calculating the expected value, which is crucial for determining the overall feasibility of the product launch.
Step 3: Calculating the Expected Value
The expected value is calculated using the formula: E(X) = P(success) * revenue(success) + P(failure) * revenue(failure). Plugging in the numbers:
- E(X) = 0.75 * $44,000 + 0.25 * (-$196,000)
- This simplifies to E(X) = $33,000 – $49,000 = -$16,000.
Since the expected value is negative at -$16,000, it indicates that the company should not proceed with making the product, as it is likely to incur a loss.