3. Box A contains 6 red balls and 3 green balls, whereas box Bcontains 3 red ball and 15 green balls.
Stage one:One box is selected at random in sucha way that box A is selected with probability 1/5 and box B isselected with probability 4/5.
Stage two: First, suppose that 1 ball isselected at random from the box selected at stage one.
a) What is the probability that the ball is red?
b) Given that the ball is red, what is the probability it camefrom box A? Next, suppose that two balls are selected at randomwithout replacement from the box selected at stage one.
c) What is the probability that both balls are red?
d) Given that both balls are red, what is the probability theycame from box A?
e) What is the probability that one ball is red and the other isgreen?
f) Given that one ball is red and the other is green, what isthe probability they came from box A?
