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	Choose the correct choice from the following answers.
A) 23/42
B) 19/42
C) 7/32
D) 16/39
E) 17/39
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, therefore   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 = 4/7   P[A/E2] = Probability of drawing a red ball when the second bag has been selected = 2/6   Using the law of total probability, we have   P(red ball) = P(A) = P(E1)P(A/E1)+ P(E2)P(A/E2)   = 1/2x4/7x + 1/2x2/6 = 19/42   Answer is 19/42
<result>B</result>
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