Bag P contains 6 red and 4 blue balls and bag Q contains 5 red and 6 blue balls. A ball is transferred from bag P to bag Q and then a ball is drawn from bag Q . What is the probability that the ball drawn is blue?

Step-by-step solution

Let E₁, E₂ and A be the events defined as follows: E ₁= red ball is transferred from bag P to bag Q E ₂= blue ball is transferred from bag P to bag Q A = the ball drawn from bag Q is blue As the bag P contains 6 red and 4 blue balls, P (E₁ )= 6 10 = 3 5 and P (E₂ )= 4 10 = 2 5 Note that E₁ and E₂ are mutually exclusive and exhaustive events. When E₁ has occurred i.e., a red ball has already been transferred from bag P to Q , then bag Q will contain 6 red and 6 blue balls, So, P (A E₁ )= 6 12 = 1 2 When E₂ has occur