Urn I holds red and white balls; urn II holds red and white balls. Two balls are drawn at random from urn I and put into urn II, then one ball is drawn at random from urn II and it is red. What is the probability that both transferred balls were red?

Answer and explanation

Correct answer: A. 4/11

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  1. Step 1: Let denote the number of red balls transferred from Urn I (containing red and white, total ) to Urn II (initially red and white, total ).
  2. Step 2: Compute the prior probabilities of transferring red balls:
  3. Step 3: After transfer, Urn II contains balls, of which are red. The likelihood of drawing a red ball from Urn II given is . The total probability of drawing a red ball is:
  4. Step 4: Apply Bayes' theorem to find :
Answer
4/11.
Why not the others: is the unconditioned prior probability , and is the conditional probability without applying Bayes' rule.

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