Answer with explanation
Two events A and B are said to be Independent ,if occurrence of one of them does not affect the occurrence of other.
For, example: A die is thrown once.Find the Probability of getting multiple of,2 and Probability of getting multiple of 3. Check whether these two events are Independent or not.
Probability of getting multiple of 2, when a die is thrown once ={2,4,6}
[tex]=\frac{3}{6}\\\\=\frac{1}{2}[/tex]
Probability of getting multiple of 3, when a die is thrown once ={3,6}
[tex]=\frac{2}{6}\\\\=\frac{1}{3}[/tex]
[tex]A\cap B={6}\\\\ P(A \cap B)=\frac{1}{6}\\\\P(A) \times P(B) =\frac{1}{2}\times\frac{1}{3}\\\\=\frac{1}{6}\\\\=P(A\cap B)[/tex]
So, if [tex]P(A \cap B)=P(A) \times P(B)[/tex]
Then ,events A and B are Independent events.