 Hello and welcome to the session. Let us discuss the following question. Question says a bag contains three red balls and five black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is red? What is the probability that the ball drawn is not red? First of all let us understand that probability of occurrence of an event E denoted by P E is equal to number of outcomes favorable to E upon total number of possible outcomes. Also probability of event E plus probability of not E is equal to 1. Now here E bar stands for not E. E and not E are complementary events. Now we will use these two expressions as our key idea to solve the given question. Let us now start with the solution. Now we are given that a bag contains three red balls and five black balls. So total balls present in the bag is equal to 3 plus 5 that is 8. Now out of these 8 balls one can be chosen in 8 ways. So total number of possible outcomes is equal to 8. Now we are given in the question that a ball is drawn at random from the bag and we are required to find probability of getting red ball. So we know number of red balls in the bag is equal to 3. Now one red ball can be drawn in three ways. Clearly we can see in the figure these are three red balls. Ball drawn at random can be this ball. It can be this ball or it can be this ball. So there are three ways in which red ball can be drawn. So in this case total number of favorable outcomes is equal to 3. From key idea we know probability of an event E is equal to number of outcomes favorable to E upon total number of possible outcomes. Now we have to find probability of getting red ball. Now here total number of favorable outcomes is equal to 3 and total number of possible outcomes is equal to 8. So probability of getting red ball is equal to total number of favorable outcomes upon total number of possible outcomes that is 3 upon 8. So we get probability that the ball drawn is red is equal to 3 upon 8. Now this completes the first part of the question. Let us now start with the second part. Now we have to find the probability that the ball drawn is not red. Now clearly we can see these two are complementary events and we know some of probabilities of complementary events is equal to 1. So we can write probability of red ball plus probability of not red ball is equal to 1. Now we know probability of red ball is equal to 3 upon 8. So we can write 3 upon 8 plus probability of not red ball is equal to 1. Now subtracting 3 upon 8 from both the sides of this expression we get probability of not red ball is equal to 1 minus 3 upon 8. Now subtracting these two terms by taking their LCM we get 8 minus 3 upon 8 which is further equal to 5 upon 8. So we get probability of not red ball is equal to 5 upon 8. So we get the probability that the ball drawn is not red is equal to 5 upon 8. This completes the second part of the question. Now the required answer is 3 upon 8 for the first part and 5 upon 8 for the second part. This completes the session. Hope you understood the solution. Take care and have a nice day.