Question

Use the following table to find the probability that a randomly chosen member of the Student Government Board is a freshman or lives in off-campus housing Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

Since the events are not mutually exclusive, the probability becomes

`Pr(\text{freshman or off-campus)}=Pr(\text{freshman)}+Pr(\text{Off}-\text{campus)}-Pr(\text{Freshman\&Off}-\text{campus)}`

Sample space = 23

Pr(Freshman) = 5/23

Pr(Off-campus) = 14/23

Pr(Freshman&Off-campus) = 3/23

Thus,

Pr( Freshman or Off- Campus) = 5/23 +14/23 - 3/23 = 16/23

Final answer = 16/23