Question

23) Of the students at Grandview State College: 60% are female 10% are biz-majors from California 25% are biz-majors 20% are females from California 30% are from California 15% are female biz-majors Which pair of events are independent? a)F& B b)F& C c) B & C d) no pair is independent

Answer 1

F denotes female students

B denotes students having biz-majors

C denotes students from California

(a) P(F and B) = percentage of female biz majors/100 = 0.15

P(F) = 0.6, P(B) = 0.25

Thus, P(F)*P(B) = 0.15 = P(F and B)

So, F & B are independent

(b) P(F and C) = 0.2 but P(F)*P(C) = 0.6*0.3 = 0.18

So, F & C are not independent

(c) P(B and C) = 0.1 but P(B)*P(C) = 0.25*0.3 = 0.075

So, B & C are not independent

Thus, option (a) is the correct answer.