A bag P contains 5 white marbles and 3 black marbles. Four marbles are drawn at random from P and are put in an empty bag Q . If a marble drawn at random from Q is found to be black then the probability that all the three black marbles in P are transfered to the bag Q is.

Step-by-step solution

Here, W= White, B= Black. Given that bag P contains 5 W marbles and 3 B marbles. 4 marbles are drawn from the bag P and A black marble is drawn from bag Q . Let Event E₁: 1 ~W and 3 ~B marbles are transferred Event E₂: 2 ~W and 2 ~B marbles are transferred Event E₃: 3 ~W and 1 ~B marbles are transferred Event E₄: 4 ~W and 0 ~B marbles are transferred and Event A : a black marble is drawn from bag Q . Then, P (E₁ )= ^5 C₁ ^3 C₃ ^8 C₄ = 5 ^8 C₄ aligned & P (E₂ )= ^5 C₂ ^3 C₂ ^8 C₄ = 30 ^8 C₄ & P (E₃ )= ^5 C₃ ^3 C₁ ^8