Question

Three bags contain a number of red and white balls as follows:
• Bag I: 3 red balls
• Bag II: 2 red balls and 1 white ball
• Bag III: 3 white balls The probability that bag \( i \) will be chosen and a ball is selected from it is \( \frac{i}{6}, i = 1, 2, 3 \). If a white ball is selected, what is the probability that it came from Bag III?

• A. \( \frac{9}{11} \)
• B. \( \frac{2}{11} \)
• C. 0
• D. \( \frac{1}{11} \)

Hint:

Bayes' Theorem is useful for finding conditional probabilities. When dealing with probabilities of multiple events, use the law of total probability to find the overall probability before applying Bayes' Theorem.

Answer 1

The Correct Option is A