A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $525,000 if successful and a 1 yearly loss of $175,000 otherwise. The probability of success is . If the second mall is selected, it is estimated that the yearly profit will be $350,000 if successful; otherwise, the annual loss will be $105,000. The probability of success at the second mall is . Complete parts (a) through (c) below a What is the expected profit for the first mall?
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.
Question 7
![**Title: Expected Profit Calculation for Retail Store Opening**
**Problem Context:**
A store specializing in mountain bikes is considering opening in one of two malls. The financial outcomes for each potential location are as follows:
- **First Mall:**
- If successful, the store anticipates a yearly profit of $525,000.
- If unsuccessful, there will be a yearly loss of $175,000.
- Probability of success: \( \frac{1}{2} \).
- **Second Mall:**
- If successful, the yearly profit is estimated at $350,000.
- If unsuccessful, the annual loss will be $105,000.
- Probability of success: \( \frac{3}{4} \).
**Tasks:**
a. **Calculate the Expected Profit for the First Mall:**
To determine the expected profit, consider both potential outcomes (success and failure) and their respective probabilities.
**Calculation for First Mall:**
- **Profit if Successful:** $525,000
- **Loss if Unsuccessful:** -$175,000
- **Probability of Success:** \( \frac{1}{2} \)
- **Probability of Failure:** \( \frac{1}{2} \) (since total probability must equal 1)
**Expected Profit Calculation:**
\[ \text{Expected Profit} = (525,000 \times \frac{1}{2}) + (-175,000 \times \frac{1}{2}) \]
**Input:**
Enter your answer in the provided answer box and click "Check Answer" to validate your calculation.
**Note:** Ensure all computations are double-checked for accuracy before submission.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275de5f4-638b-4b28-b8d0-84d4784ec7ed%2F3bf941a7-01ff-49ac-b3e7-e888d32ed9a4%2F9qqcbeq_processed.jpeg&w=3840&q=75)
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