Question

Let A and B be two disjoint events in S. Suppose that Pr(A) = p, Pr(B) = q and Pr(A U B) = r.

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

A) r2 < pq / 4

B) pq / 4 ≤ r2 ≤ pq

C) pq ≤ r2 ≤ 4pq

D) r2 > 4pq ​

Answer 1

Step-by-step explanation:

11th

Maths

Probability

Algebra of Events

Suppose A and B are two eve...

MATHS

Suppose A and B are two events with P(A)=0.5 and P(A∪B)=0.8. Let P(B)=p if A and B are mutually exclusive and P(B)=q if A and B are independent events, then the value of q/p is

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ANSWER

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

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