Question 1177160
<pre>
Many textbooks define independent events by that formula.  You can't prove
what is stated in a definition.

Two events A, B are said to be independent if and only if 

P(A ∩ B) = P(A)P(B).

All I can guess is that your textbook has defined it this way:

Two events A, B are said to be independent if and only if 

P(A|B) = P(A)

And the definition of conditional probability is 

P(A|B) = P(A ∩ B)/P(B).

If so, you can prove it by substituting P(A) for P(A|B)

P(A) = P(A ∩ B)/P(B)

and then multiplying both sides by P(B)

P(A)P(B) = P(A ∩ B)

Edwin</pre>