Answer to Question #208963 in Statistics and Probability for mimi

Question

If A and B are independent events, then P .A and B/ D P.A/
P .B/

Answer 1

We know that,

If A and B are independent events then,

$P(A/B)=P(A)\\P(B/A)=P(B)\ \ and\\P(A \ and \ B)=P(A)\cdot P(B)$

So, from the third equation we can say that,

$$\dfrac{P(A\ and\ B)}{P(A)\times P(B)}=1$$