Question

If P and Q are two random events, then the following is TRUE

• A. Independence of P and Q implies that probability $(P\cap Q)=0$
• B. Probability $(P\cup Q)\ge$ Probability (P) + Probability (Q)
• C. If P and Q are mutually exclusive, then they must be independent
• D. Probability $(P\cap Q)\le$ Probability (P)

Answer 1

The correct option is D Probability $(P\cap Q)\le$ Probability (P)

If A and B are disjoint (or mutually exclusive means $A\cap B=\varphi$) events then.

$P(A\cup B)=P\left(A\right)+P\left(B\right)$

or $P(A\cap B)=0$

For any events A and B,
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)\le P\left(A\right)+P\left(B\right)$

If A and B are independent events then

$P(A\cap B)=P\left(A\right)\times P\left(B\right)$

$P(A\cap B)\le \left\{P\right(A),P(B\left)\right\}$