Question

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 drawn ball is red.

Answer 1

consider the result as 2 independent events

bag1, red
bag2, red

Prob(bag1,red) = (1/2)(4,7) = 2/7
prob(bag2,red) = (1/2)2/6) = 1/6

prob(your event) = 2/7 + 1/6 = 19/42