A pair of events A and B cannot be simultaneously mutuallyexclusive and independ

Question

A pair of events A and B cannot be simultaneously mutuallyexclusive and independent. Prove that if P(A)>0 and P(B)>0,then:

a) If A and B are mutually exclusive, they cannot beindependent.
b) If A and B are independent, they cannot be mutuallyexclusive.

Explanation / Answer

(a) A and B are independent when P(A) x P(B) = P(A and B) Since they are mutually exclusive, P(A and B) = 0 However, P(A) >0 and P(B) > 0 Two non-zero products cannot give zero. Thus, if A and B are mutually exclusive, they cannot beindependent (b) Since A and B are independent, P(A) x P(B) = P(A and B) If the events are independent, there will be some case in whichboth A and B happens This means that P(A) x P(B) cannot be zero. Thus, if A and B are independent, they cannot be mutually exclusive(P(A and B) = 0) Hope this helps!

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.