SOLUTION: say there are 5 male undergraduates, 2 female undergrduates, 2 male graduates, and 2 female graduates. find the probability of selecting an undergraduate or a female? i thought it

Your error is because when you add the 7 undergraduates and the 4
females you are counting the 2 undergraduate females TWICE!  You are
counting them once among the 7 undergraduates and again among the
4 females.  Therefore you have to subtract those 2 once from the 7+4
to keep from counting them twice. Therefore you get  = .

You can also make a chart:

       -------------------------------------------
       |   grad   |  undergraduate   ||  totals  |
--------------------------------------------------
male   |    2     |       5          ||    7     |
--------------------------------------------------
female |    2     |       2          ||    4     |
==================================================
totals |    4     |       7          ||   11     |

You only want to count the red numbers which add up to 9,
So the probability is 

Or you can use the formula that the other tutor used:

P(U or F) = P(U) + P(F) - P(U and F)
          =  +  - 
          = 

Edwin