Question

Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him.

Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black stacks, one pair of grey stacks, and one red tie. All six of his possible outfits are listed below.

Let A be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and B be the event that he selects an outhit with a black shirt

What is P(A or B), the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt?

Shirt Slacks Tie
Outfit 1 Blue Black Red
Outfit 2 Blue Grey Red
Outfit 3 White Black Red
Outfit 4 White Grey Red
Outfit 5 Black Black Red
Outfit 6 Black Grey Red

Answer 1

Mark's little brother has a 50% chance of selecting either an outfit with a white shirt and grey slacks or an outfit with a black shirt. The probability of the first event is 1/6, and the probability of the second event is 1/3. Since they are mutually exclusive events, we add these probabilities to get 1/2.

Step-by-step explanation:

Mark's little brother must select an outfit for him, and we want to calculate the probability P(A or B), where event A is selecting an outfit with a white shirt and grey slacks, and event B is selecting an outfit with a black shirt. From the given list of outfits, we see that:

• Outfit 4 corresponds to event A (white shirt with grey slacks).
• Outfit 5 and Outfit 6 correspond to event B (any outfit with a black shirt).

Since there are 6 possible outfits, each with an equal chance of being selected, the sample space contains 6 outcomes. Therefore, the probability of event A is P(A) = 1/6, since only one of the six outfits corresponds to it.

Similarly, the probability of event B is P(B) = 2/6 or 1/3, since two of the six outfits correspond to selecting a black shirt.

The events A and B are mutually exclusive since one outfit cannot be simultaneously white with grey slacks and have a black shirt. Thus we add the probabilities of A and B to get P(A or B).

Therefore, P(A or B) = P(A) + P(B) = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.

So there is a 50% chance that Mark's little brother will select either an outfit with a white shirt and grey slacks or an outfit with a black shirt.