There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A fair die is cast, if the face 1 or 3 turns up, a ball is taken from the first bag, and if any other face turns up a ball is chosen from the second bag. Find the probability of choosing a black ball.

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from lot.

A box contains 4 white and 3 black balls. Another box contains 3 white and 4 black balls. A die is thrown. If it exhibits a number greater than 3 , the ball is drawn from the first box. Otherwise, a ball is drawn from the second box. A ball drawn is found to be black. The probability that it has been drawn from the second box is

There are two Urns. The first one contains 4 white and 6 blue balls and the other contains 4 white and 5 blue balls. One of the urns is selected at random and a ball is drawn. If the ball drawn is white, find the probability that it is drawn from the first urn.

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

An urn contains 6 white and 4 black balls. A fair die is rolled and that number of balls we chosen from the urn. Find the probability that the balls selected are white.