Answer to Question #177270 in Statistics and Probability for deepak

Question

For two independent events A and B, if P(A) = 2.0 and P(B) = 4.0, then 

(A∩ B) =0 .6

Check either true or false with shirt proof or counter example

Answer 1

Events A and B are independent if

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

If A and B are not independent then they are dependent.

In this case:

P(A)= 2.0

P(B)=4.0

and P($A\cap B$ )= 0.6

Now, applying condition

P(A)$\times P(B)$ = 2.0$\times$ 4.0= 8.0 which is not equal to $P(A\cap B)$

So, Events A and B are dependent events.