Question

Example 31 For any sets A and B, show that
P(
AB)=P(A) P( B ).​

Answer 1

$\huge\boxed{\underline{\underline{\green{Solution}}}} </p><p>$

The required result is possible if A & B mutually Independent Events

Now

A & B are two mutually Independent Events

So

$P (\frac{A}{B} ) = P(A)$

Now from the definition of Conditional Probability

$P (\frac{A}{B} ) = \frac{P(A \cap \: B)}{P(B)}$

$\implies \: P(A) = \: \frac{P(A \cap \: B)}{P(B)}$

$\therefore \: P(A \cap \: B)=P(A) P( B ).$

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