Need help in probability of 2 or more events

Hi!

Please provide the source and answer choices for all of your questions. Spoilers with the correct answers aren't very useful without the choices! Further, the answers often provide valuable hints as to how you should proceed.

In any case:

Probability = (# of desired outcomes)/(total # of possibilities)

Here, there are 900 students in total, so that will be our denominator. The numerator will be the # of students that match our requirements: male (any) or female that's over 16 years old. Accordingly, our equation becomes:

Probability = (# of males + # of females over 16)/(total # of students)

As you noted, there are 500 males. When you did your calculation, however, you set the number of females over 16 to 400; that's the total number of females, not the ones that we want to select. According to the question stem, there are only 80 females over 16. So, our numerator will be 500 + 80 = 580.

Consequently, the correct answer is:

580/900 = 58/90 = 29/45

As an important aside, the question isn't properly written. On the GMAT, the question would certainly let us know that the selection of a grant recipient is random - without that explicitly stated, there is no correct answer to the question. So, to be a proper question, it should read: