By Baye's theorem, which one of the following probabilities is calculated?

Options

A. Prior probability
B. Likelihood probability
C. Posterior probability
D. Conditional probability

Answer

To solve the question regarding which probability is calculated by Bayes' theorem, we can follow these steps:

### Step 1: Understand Bayes' Theorem
Bayes' theorem is a mathematical formula used to determine conditional probabilities. It relates the conditional and marginal probabilities of random events.

### Step 2: Identify the Formula
The formula for Bayes' theorem can be expressed as:
\[ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} \]
Where:
- \( P(A|B) \) is the probability of event A occurring given that B is true.
- \( P(B|A) \) is the probability of event B occurring given that A is true.
- \( P(A) \) is the probability of event A occurring.
- \( P(B) \) is the probability of event B occurring.

### Step 3: Recognize the Application
Bayes' theorem is primarily used to calculate the conditional probability \( P(A|B) \). This means it helps us find the probability of one event occurring given that another event has occurred.

### Step 4: Conclusion
From the understanding of Bayes' theorem, we can conclude that it is used to calculate conditional probabilities. Therefore, the correct answer to the question is that Bayes' theorem is used to calculate the conditional probability \( P(A|B) \).