Let E_{1}, E_{2}, E_{3}, …………. E_{n} mutually exclusive and exhaustive events and A is dependent event occurs after E_{1}, E_{2}, E_{3}, …………. E_{n}.
Probability of event A
By multiplication theorem
.
Where stands for probability of event A, if it is given that event already occurs.
Example 1:  A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red. 
Solution: 
Let E_{1} : Selecting bag 1 E_{2} : Selecting bag 2 A : Drawing red ball

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