Bowl I contains 7 red and white chips and bowl II has 4 red and 6 white chips. Two chips are selected at random and without replacement from I and transferred to II. Three chips are then selected at random and without replacement from II.
a. What is the probability that all three are white?
b. Given that three white chips are selected from II, what is the conditional probability that two white chips were transferred from I?
Best Answer
Hint for (a): use the law of total probability, conditioning over which two chips are transferred.
Then for (b), Bayes' theorem gives \begin{equation} P(\text{2 transferred} \mid \text{3 selected}) = \frac{P(\text{3 selected} \mid \text{2 transferred})P(\text{2 transferred})}{P(\text{3 selected})}. \end{equation} The two terms in the numerator should be easy; the denominator is your answer from part (a).