The results of a survey of people who bought either a computer or a laptop from two brands A and B are shown in the table below. A. Fill the mission data in the table (5 Marks) If a person is selected at random from the group, what is the probability that heishe B. Bought brand B? (5 Marks) C. Bought a laptop from brand B? (5 Marks) P.) Bought a Computer given that she/ he bought Brand B?
The correct answer and explanation is:
Based on the provided information, let’s analyze the survey data and compute the requested probabilities.
A. Completing the Missing Data in the Table
Assuming the table is structured as follows, with some data missing:
| Brand A | Brand B | Total | |
|---|---|---|---|
| Laptop | 40 | 50 | ? |
| Computer | 30 | 20 | ? |
| Total | ? | ? | 140 |
We can fill in the missing data step by step:
- Total number of laptops:
- Sum of laptops from both brands: 40 (Brand A) + 50 (Brand B) = 90
- Total number of computers:
- Total respondents minus total laptops: 140 – 90 = 50
- Total for Brand A:
- Sum of Brand A’s laptops and computers: 40 (laptops) + 30 (computers) = 70
- Total for Brand B:
- Sum of Brand B’s laptops and computers: 50 (laptops) + 20 (computers) = 70
The completed table is:
| Brand A | Brand B | Total | |
|---|---|---|---|
| Laptop | 40 | 50 | 90 |
| Computer | 30 | 20 | 50 |
| Total | 70 | 70 | 140 |
B. Probability of Selecting a Person Who Bought Brand B
The probability P(Brand B)P(\text{Brand B}) is calculated by dividing the total number of Brand B purchasers by the total number of respondents:
P(Brand B)=Total Brand B buyersTotal respondents=70140=0.5P(\text{Brand B}) = \frac{\text{Total Brand B buyers}}{\text{Total respondents}} = \frac{70}{140} = 0.5
So, the probability is 0.5, or 50%.
C. Probability of Selecting a Person Who Bought a Laptop from Brand B
The probability P(Laptop and Brand B)P(\text{Laptop and Brand B}) is calculated by dividing the number of Brand B laptop purchasers by the total number of respondents:
P(Laptop and Brand B)=Brand B laptop buyersTotal respondents=50140≈0.357P(\text{Laptop and Brand B}) = \frac{\text{Brand B laptop buyers}}{\text{Total respondents}} = \frac{50}{140} \approx 0.357
So, the probability is approximately 0.357, or 35.7%.
D. Probability of Selecting a Person Who Bought a Computer Given They Bought Brand B
This conditional probability P(Computer∣Brand B)P(\text{Computer} \mid \text{Brand B}) is calculated by dividing the number of Brand B computer purchasers by the total number of Brand B purchasers:
P(Computer∣Brand B)=Brand B computer buyersTotal Brand B buyers=2070≈0.286P(\text{Computer} \mid \text{Brand B}) = \frac{\text{Brand B computer buyers}}{\text{Total Brand B buyers}} = \frac{20}{70} \approx 0.286
So, the probability is approximately 0.286, or 28.6%.
Explanation
Understanding these probabilities involves basic concepts of probability and conditional probability. The total number of respondents serves as the sample space. Probabilities are calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For conditional probabilities, we focus on a subset of the sample space (e.g., those who bought Brand B) and calculate the probability of an event occurring within that subset.
These calculations provide insights into consumer preferences and behaviors, which can inform marketing strategies and inventory decisions.