Bag I holds 3 red and 2 white balls; bag II holds 1 red and 4 white balls. A bag is chosen at random and a ball drawn is red. What is the probability that it came from bag I?
Answer and explanation
Correct answer: A.
- Step 1: and , and each bag has probability .
- Step 2: By Bayes' theorem .
Answer
.
Why not the others: : only was used, with no conditioning. : the choice of bag was assumed independent of the colour. : this is the probability for bag II.
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