There are two bags. One bag contains six green and three red balls. The second bag contains five green and four red balls. One ball is transferred from the first bag to the second bag. Then one ball is drawn from the second bag. Find the probability that it is a red ball.

Bag A contains $5$ white and $4$ black balls, and bag B contains $7$ white and $6$ black balls. One ball is drawn from bag A and without noticing its colour, is put in the bag B. If a ball is then drawn from bag B, find the probability that it is black in colour.

An urn contains $5$ red and $5$ black balls. A ball is drawn at random, its colour is noted and is then returned to the urn. Moreover, $2$ additional balls of the same colour are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

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 die is thrown. If it shows up $1$ or $3$, a ball is taken from the first bag; but if it shows up any other number, a ball is chosen from the second bag. Find the probability of choosing a black ball.

Urn I has $2$ white and $3$ black balls, urn II has $4$ white and $1$ black ball and urn III has $3$ white and $2$ black balls. An urn is selected at random and a ball is drawn at random. What is the probability of drawing a white ball?

In a factory, a product is manufactured by any of three machines A, B and C. They produce respectively $25\%$, $35\%$ and $40\%$ of the total products. A product is selected at random. Find the probability that it is defective. Assume that machines A, B and C produce respectively $5\%$, $4\%$ and $2\%$ defective items.

Bag A contains $1$ white, $2$ blue and $3$ red balls. Bag B contains $3$ white, $3$ blue and $2$ red balls. Bag C contains  $2$ white, $3$ blue and $4$ red balls. One bag is selected at random, and then two balls are drawn from the selected bag. Find the probability that the balls drawn are white and red.

An urn contains $2$ white and $2$ black balls. A ball is drawn at random. If it is white, it is not replaced. If it is black, then it is replaced along with one additional ball of the same colour. This process is repeated. Find the probability that the third ball drawn is black.

There are two bags I and II. Bag I contains $2$ white and $4$ red balls and bag II contains $5$ white and $3$ red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.