Does the following table represent a probability distribution?
| Category | Probability |
| -------- | ----------- |
| Main Dish | 0.421 |
| Appetizer | 0.210 |
| Dessert | 0.103 |
| Salad | 0.173 |
| Vegetable | 0.093 |
A. No
B. Yes
C. Can't be determined with the given information
Answer (2)
Yes, the table represents a probability distribution as the sum of all provided probabilities equals 1. Each probability value is between 0 and 1, satisfying the conditions for a probability distribution. Hence, the answer is Yes.
;
Calculate the sum of the probabilities: 0.421 + 0.210 + 0.103 + 0.173 + 0.093 = 1.0 .
Verify that the sum equals 1.
Since the sum is 1, the table represents a probability distribution.
The answer is Yes. Y es
Explanation
Analyze the problem We are given a table with five recipe categories and their associated probabilities. To determine if this table represents a probability distribution, we need to check if the sum of all probabilities equals 1.
Calculate the sum of probabilities Let's calculate the sum of the probabilities: S = 0.421 + 0.210 + 0.103 + 0.173 + 0.093
Verify if the sum equals 1 The sum of the probabilities is: S = 1.0 Since the sum of the probabilities equals 1, the table represents a probability distribution.
Conclusion Since the sum of the probabilities is equal to 1, the table represents a probability distribution.
Examples
Probability distributions are used in many real-life scenarios. For example, in weather forecasting, probabilities are assigned to different weather conditions (sunny, rainy, cloudy, etc.) to predict the likelihood of each condition occurring. Similarly, in finance, probability distributions are used to model the potential returns of investments, helping investors make informed decisions. In quality control, probability distributions help assess the likelihood of defects in a manufacturing process, ensuring product quality. Understanding probability distributions allows us to make predictions and informed decisions in various fields.
