Answer:
[tex]\frac{8}{17}[/tex]
Explanation:
Here, we want to get the probability that a randomly chosen member of the student government Board is a sophomore or lives in off-campus housing
What we need to do here is to sum the count of sophomores and students living in off-campus housing, then divide it by the total number of students
Mathematically, we have that as;
[tex]\frac{4}{17}+\text{ }\frac{5}{17}-\frac{1}{17}\text{ = }\frac{8}{17}[/tex]
We are subtracting the 1/17 because we have sophomores who live off campus:
[tex]P(A\text{ U B\rparen = P\lparen A\rparen + P\lparen B\rparen -P\lparen A n B\rparen}[/tex]
P(A) refers to the probability of selecting a sophomore
P(B) refers to the probability of off-campus housing
P(A n B) refers to the probability of a sophomore who lives off campus
