Bayes Theorem

Let
By Bayes' theorem,

Step 1: Understanding the Concept:
This problem is a classic application of Bayes' Theorem. We are given the prior probabilities of visiting each temple and the conditional probabilities of meeting a friend. We need to find the posterior probability of visiting Temple B, given that the event "meeting a friend" has already occurred.

Step 2: Key Formula or Approach:
Bayes' Theorem:

Step 3: Detailed Explanation:
1. Define the events: - : Visits Temple A, : Visits Temple B, : Meets her friend. 2. Given probabilities: - . - Since she visits only one temple, . - (Meeting friend at A). - (Meeting friend at B). 3. Calculate Total Probability of meeting her friend : Find common denominator (105): 4. Apply Bayes' Theorem for Temple B:

Step 4: Final Answer
The probability that she met her friend at temple B is .