 Hello friends and how are you all doing today? The question says an urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that firstly both the balls are red. Secondly one ball is red the other is black. Thirdly one ball is white. Right, so let us proceed with our solution. Firstly we are given number of white balls 7, then we are given number of black ball 5 and then we are given number of red balls 3. So this means total number of balls will be equal to 7 plus 5 plus 3 that gives us 15. Now with the help of this information we will be finding out the probability of these three. Now firstly We need to find out the probability that both the balls are red. So it will be equal to there are three red balls and out of which we are taking out two red balls divided by there are 15 balls in totality and we need to take out two balls from these 15 balls. So this is equal to 3 into 2 divided by 15 into right 14. On simplifying we have the answer to the first part as 1 by 35. Right, so this completes the first part. Now let us proceed with the second part. Now here we need to find out the probability that one ball that we have taken out is red and the other is black. So the probability of occurring this event will be equal to 3 into 5 into 2 divided by 15 C 2. Right, so this is equal to 3 into 5 into 2 divided by 15 into 14. That gives us the answer to the second part as 1 by 7. So the probability that we will pick out one ball that is red and the other is black is 1 by 7. This completes the second part. Let us proceed to do the last part. Now here we need to find out the probability that one ball is white. So it will be equal to 7 into 8 into 2 divided by 15 into 14. That is 15 C 2 itself. That is further equal to 8 by 15. Because on simplifying these three terms will get cancelled out and we are left with the answer that is 8 by 15. Right, so this completes the third part and the solution to hope you understood the whole concept well and enjoyed it to have a nice day.