An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $60,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes into recession, the investment will result in a loss of $60,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70% probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment? The expected profit is $ (Type an integer or a decimal.)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![**Scenario: Investment Decision Based on Economic Predictions**
An investment counselor provides a stock tip, suggesting different outcomes based on the economic climate. The potential outcomes are:
- **Strong Economy:** Profit of $60,000
- **Moderate Economic Growth:** Profit of $10,000
- **Recession:** Loss of $60,000
An economist provides the following probabilities:
- **20%** chance the economy will remain strong
- **70%** chance the economy will grow moderately
- **10%** chance of recession
**Question:** What is the expected profit from this investment?
**Calculation of Expected Profit:**
To find the expected profit, use the formula for expected value, which is the sum of all possible profits weighted by their probabilities:
\[
\text{Expected Profit} = (0.20 \times 60,000) + (0.70 \times 10,000) + (0.10 \times -60,000)
\]
Perform the calculations:
- Strong Economy: \(0.20 \times 60,000 = 12,000\)
- Moderate Growth: \(0.70 \times 10,000 = 7,000\)
- Recession: \(0.10 \times -60,000 = -6,000\)
Sum these values to get the expected profit:
\[
\text{Expected Profit} = 12,000 + 7,000 - 6,000 = 13,000
\]
Therefore, the expected profit is **$13,000**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2a79f3c-9d5f-475d-8512-37c872933c1c%2F3c1bf77d-d52e-4845-a398-8d8aa614842d%2F709z51c_processed.png&w=3840&q=75)
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