
Homework Question
Here's the question:
A package, say A, of 24 crocus bulbs contains 8 yellow bulbs, 8 white, and 8 purple. Another package, say B, of 24 crocus bulbs contains 6 yellow, and 6 white, 12 purple crocus bulbs. One of the two packages is selected at random.
(a) If three bulbs from this package were planted and all three yielded purple flowers, compute the conditional probability that package B was selected.
(b) If the three bulbs yielded one yellow flower, one white flower, and one purple flower, compute the probability that package A was selected.
I have the answer given in the book [(220/276) and (512/944)], but I cannot find how to get it. I've tried several different methods and can't match the answer.
Can anyone help? Please...

Part a: $\displaystyle P\left( {Bp} \right) = \frac{{P\left( {pB} \right)P(B)}}{{P\left( {pB} \right)P(B) + P\left( {pA} \right)P(A)}}
$.
Can you compute that?