A bag contains 4 red ball 5 black ball and Bag B contains 3 red and 7 black ball . one ball is drawn from bag A and two balls drawn from bag b . find the probability that out of three balls drawn two are black and one is red.

To find the probability of drawing two black balls and one red ball, we need to calculate the probability of each individual event and then multiply them together.

Let's start with the probability of drawing two black balls from Bag B. Bag B contains a total of 10 balls (3 red + 7 black), so the probability of drawing the first black ball is 7/10. After the first black ball is drawn, there are 9 balls left in the bag, including 6 black balls. Therefore, the probability of drawing a second black ball is 6/9.

Now, let's move to the probability of drawing a red ball from Bag A. Bag A contains a total of 9 balls (4 red + 5 black), so the probability of drawing a red ball is 4/9.

Since we have two independent events (drawing two black balls from Bag B and one red ball from Bag A), we can multiply their probabilities together to get the overall probability:

Probability = (Probability of drawing two black balls from Bag B) * (Probability of drawing one red ball from Bag A)
= (7/10) * (6/9) * (4/9)
= 168/810
= 28/135

Therefore, the probability that out of the three balls drawn, two are black and one is red is 28/135.