Suppose you have a bag with 6 blue marbles and 4 red marbles. Calculate the following probabilities: a) If you randomly remove half of the marbles from the bag, what is the probability that 3 of them...

Suppose you have a bag with 6 blue marbles and 4 red marbles. Calculate
the following probabilities:
a) If you randomly remove half of the marbles from the bag, what is the probability that 3 of them are blue and 2 are red?
b) Suppose that you sample with replacement from the bag: you take out a marble, record its color, then throw it back in. What is the probability that you need to repeat this process exactly 10 times before seeing your first red marble on your 10th selection?
c) Again sampling with replacement, what is the probability that you need to repeat the process exactly 10 times before seeing your 4th red marble on your 10th selection?
d) Again sampling with replacement, what is the probability that if you sample 10 times, exactly 4 of your marbles are red?