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.

A red ball can be drawn in two mutually exclusive ways.

I.  Selecting bag I and then drawing a red ball from it.

II. Selecting bag II and then drawing a red ball from it.

Let E₁, E₂ and A denote the events defined as follows:

E₁ = selecting bag I,                

E₂ = Selecting bag II, 

A = Drawing a red ball

Since one of the two bags is selected randomly.