For the following pair of events, (a) determine if the two events A and B are mutually exclusive, and (b) find the probability that A or B (or both) happens.
Penny has a green shirt, a purple shirt, and a red shirt. Seemingly, she shops at the same place where Jenny bought her shoes. Penny also has black pants and blue pants. She picks a shirt at random and picks a pair of pants at random. What an appearance-conscious fashionista she is.
Hey, it was dark when she got dressed. Cut her some slacks.
Event A: Penny wears a green shirt.
Event B: Penny wears black pants.