Suppose that a certain college class contains 61 students Of

Suppose that a certain college class contains 61 students. Of these, 37 are seniors, 34 are physics majors, and 6 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a senior and a physics major? (b) Given that the student selected is a senior, what is the probability that she is also a physics major? Write your responses as fractions. (If necessary, consult a list of formulas.)

Solution

Total students=61

senior=37

physics major = 34

6 are neither

so senior or Physics major = 61-6=55

senior and Physics major = 37+34-55=16 ( P( A AND B) = P(A)+P(B)-P(A OR B))

a). P( both senior and physics major) = 16/61

b).P( Physics major/ senior) =16/37