Question

If A and B are two independent events in a sample space S ,then $P(A\cap B)=$

• A. $P\left(A\right).P\left(\frac{A}{B}\right)$
• B. $P\left(B\right).P\left(\frac{B}{A}\right)$
• C. $P\left(A\right).P\left(B\right)$
• D. $P\left(A\right)+P\left(B\right)$

Answer 1

Answer: (C)

$P\left(A\right).P\left(B\right)$

$\frac{P(A\cap B)}{P\left(B\right)}=P\left(A|B\right)$
If A and B are two independent events then: $P\left(A|B\right)=P\left(A\right)$
$P(A\cap B)=P\left(A\right)P\left(B\right)$