A box contains 5 black shirts, 9 blue shirts, 7 black pants, and 8 blue pants. Determine the probability of randomly selecting a black piece of clothing or a shirt.

Question

  Use P(A or B)= P(A and B) to explain your answer.

Answer 1

P(A or A) = P(A) + P(B)

P(A) = 7 / 29

P(B) = 9 / 29

P(A or B) = 16 / 29

Answer 2

Let A be the outcome in which we draw a black piece of clothing, and B be the outcome in which we drew a shirt.

We can define the probability of an event E occuring from a given sample space S (sample space refers to the set of all possible outcomes) as being equal to the number of outcomes within E divided by the number of outcomes within S.

Using this, we can see that P(A) = probability of drawing a black piece of clothing = 12/29 (since we have 5+7=12 black items, and 5+7+9+8=29 items total).

P(B) = 14/29 following the same reasoning.

Now, to answer the question, P(A or B) = P(A) + P(B) - P(A and B). The reason for subtracting the last term is because you don't want to double count outcomes (which, in our example, are pieces of clothing that are both black and shirts).

So, P(A or B) = 12/29 + 14/29 - 5/29 = 21/29 and this is our final answer (5/29 refers to the 5 pieces where are both black and shirts).

Hope this sort of long explanation helps!