An apartment building has the following distribution of apartments:
1 bedroom 2 bedroom 3 bedroom
1st floor 3 1 1
2nd floor 2 2 2
3rd floor 1 4 1
If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?
A) 7/11
B) 6/11
C) 13/17
D) 11/17

Question

An apartment building has the following distribution of apartments:           
                  1 bedroom   2 bedroom	   3 bedroom 
1st floor	        3                   1                     1 
2nd floor	        2                   2                     2 
3rd floor	        1                   4                     1
If an apartment is selected at random, what is the probability that it is on the 2nd floor or has 2 bedrooms?
A) 7/11
B) 6/11
C) 13/17
D) 11/17

anonymous · Answer

How many apartments have 2 bedrooms? Looking down the middle column, 1 + 2 + 4 = 7.

How many apartments are on the second floor? Looking across the middle row, 2 + 2 + 2 = 6.

But wait! We're counting something twice: two bedroom apartments on the second floor. Means you just need to subtract it (equivalent of only counting it once).

7 + 6 - 2 = 7 + 4 = 11.

How many possibilities are there? How many apartments are there in this building? 3 + 1 + 1 + 2 + 2 + 2 + 1 + 4 + 1 = 17.

11 unique buildings match the criteria, and since there are 17 possibilities, the answer is D. 11/17.