 Hi and welcome to the session. Let's work out the following question. The question says a bag contains five red six white and seven black balls two balls are drawn at random What is the probability that both balls are red or both are black? So let's start with the solution to this question. We see that one bag has five red six white and seven black balls therefore total number of balls is equal to five plus six plus seven that is equal to 18 We have to draw two balls which are neither both red or both black balls now probability of getting both red balls is equal to five C2 divided by 18 C2 because that is a probability of choosing two balls from five red balls divided by choosing two balls from total 18 balls This is equal to five into four divided by 18 into 17 that is equal to 10 divided by 153 now probability that both are black balls is equal to 7 C2 divided by 18 C2 that is equal to 7 into 6 divided by 18 into 17 That is equal to 7 by 51 hence the probability that both are red or both black balls is given by adding these two probabilities that is equal to 10 divided by 153 plus 7 divided by 51 that is equal to 10 plus 21 divided by 153 and That is equal to 31 divided by 153 So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day