How do you solve?

Question

An apartment building has the following distribution of apartments:

	1 bedroom	2 bedroom	3 bedroom
1st floor	3	1	1
2nd floor	0	4	2
3rd floor	1	4	1

If an apartment is selected at random, what is the probability that it is not a 2 bedroom apartment on the 2nd floor?

Answer 1

To find the probability of any event happening, we can take the number of outcomes that we are interested in, and divide that by the total number of possible outcomes (including the ones we are interested in).

In this example, there are 3 + 1 + 1 + 0 + 4 + 2 + 1 + 4 + 1 = 17 apartments in total. So, you can think of 17 as the total number of possible "outcomes".

Four (4) of the apartments are 2-bedroom apartments on the 2nd floor. So, the probability of a randomly selected apartment being a 2-bedroom on the 2nd floor is 4/17, or about 0.235.

BUT, we are asked to find the probability that a randomly selected apartment is *not* a 2-bedroom apartment on the 2nd floor. There are a couple of ways to get the answer.

One way is to find the probability that the apartment is a 2-bedroom on the 2nd floor and subtract that from 1:

1 - 4/17 = 1 - 0.235 ≈ 0.765.

Alternatively, we can take the number of apartments that are *not* 2-bedrooms on the second floor and divide that by the total number of apartments:

(17 - 4)/17 = 13/17 ≈ 0.765.