A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If from the selected bag, one ball is drawn at random, then the probability that the ball drawn is red, is

Step-by-step solution

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 aligned & E₁= Selecting bag I & E₂= Selecting bag II aligned Since, one of the two bags is selected randomly. P (E₁ )= 1 2 and P (E₂ )= 1 2 Now, P ( A E₁ )= Probability of drawing a red ball when the first bag has been selected =4 / 7P ( A E₂ )= Probability of drawing a red ball when the seco