Two robots (robot A and B) are playing basketball against each other each with their own ball. Assume time is slotted and at each time slot A and B each try to shoot with probability pA and pB respectively and independently. A and B miss the shot with probability mA and mB respectively and independently.

a) Given that T is a random variable representing the number of shots successfully made in a given time slot, what is the mean of T?

b) Calculate the probability that during a single time slot at least one shot is made.

c) Calculate the probability that during N time slots no shots are made.