A game involves rolling a fair die followed by drawing a marble from either urn A or B. If the outcome is less than 3, then a marble is drawn at random from urn A. Otherwise, a
marble is drawn at random from urn B. Urn A contains 3 red marbles, 4 blue marbles,
and 3 green marbles. Urn B contains 3 red marbles and 1 blue marble.
a) Find the probability that
i. a red marble is chosen.
11. the outcome of the die is less than 3 if it is known that the marble drawn is red.
iii. it is a red or green marble.
b) The similar game is repeated but two marbles are drawn instead from either urn A or
B. Find the probability that both marbles are red if the first marble is taken
i. with replacement.
ii. without replacement.​