Question

Let A and B be two independent events in S. Suppose that Pr(A) = p, Pr(B) = q and Pr(A ∩ B)

= r. If 0 < p, q < 1, which of the following is true?

A) r < (p + q)2 / 4

B) r > (p + q)2 / 4

C) r < pq

D) r > pq

hard one......let's see who knows ​

Answer 1

Step-by-step explanation:

P(A)=0.5 and P(AB)=0.8

When A and B are independent events,

P(A∩B)=P(A)×P(B)

⇒P(A)+P(B)−P(A∪B)=0.5×q

⇒0.5+q−0.8=0.5q

⇒0.5q=0.3

⇒q=0.6

When A and B are mutually exclusive events

P(A∩B)=0

P(A)+P(B)=P(A∪B)

0.5+p=0.8

⇒p=0.3

Hence the ratio of q and p is 2