Q. Suppose the probability of David coming to a party is 75% and the probability of Jason coming to a party is 85%. What is the probability that they will both come to a party, assuming the events are independent?

Solution:

Since the events are independent, we know that
P(David and Jason) = P(David) x P(Jason) = 0.75 x 0.85 = 0.64.
There is a 64% probability that both David and Jason will come to a party.

Example: The 15 labeled pool balls are put into a large bin. One ball is selected at random and put back into the box, and then another ball is chosen at random. What is the probability that the black 8 ball is selected both times?

Solution: Since the first ball is replaced before the second is chosen, both picks are independent of each other. Thus P(8 on first) and P(8 on second) are independent.