 Hello and welcome to the session. Let us discuss the following question. Question says, a lot consists of 144 ball pins of which 20 are defective and the others are good. Moori will buy a pin if it is good but will not buy if it is defective. The shopkeeper draws one pin at random and gives it to her. What is the probability that she will buy it? What is the probability that she will not buy it? First of all, let us understand that probability of occurrence of an event E denoted by P e is defined as number of outcomes favourable to E upon total number of possible outcomes. This is the key idea to solve the given question. Let us now start with the solution. Now we know we have a lot of 144 ball pins. So one pin can be chosen in 144 ways. So we can write total number of possible outcomes is equal to 144. Now in the first part we have to find the probability that Moori will buy the pin and we know she will buy the pin if it is good. So first of all let us find out number of good pins. We know number of defective pins is equal to 20. This is given in the question. Now number of good pins is equal to total pins minus number of defective pins. It is equal to 144 minus 20 which is further equal to 124. So number of good pins is equal to 124. Now clearly we can see one good pin can be chosen in 124 ways. So number of outcomes favourable to good pin is equal to 124. From key idea we know probability of occurrence of an event is equal to number of outcomes favourable to E upon total number of possible outcomes. So probability of getting a good pin is equal to number of outcomes favourable to good pin upon total number of possible outcomes. Now we know probability of outcomes favourable to good pin is equal to 124 and total number of possible outcomes is equal to 144. So probability of getting a good pin is equal to 124 upon 144. Now we will cancel common factor 4 from numerator and denominator both and we get probability of getting a good pin is equal to 31 upon 36. Now we are given that Noory will buy a pin if it is good. So probability that Noory will buy a pin is equal to probability of getting a good pin that is 31 upon 36. So we can write probability that she will buy a pin is equal to 31 upon 36. Now this completes the first part of the given question. Now let us start with the second part. Now we have to find the probability that she will not buy a pin. Now we know Noory will not buy a pin if it is defective and total number of defective pins is equal to 20. So one defective pin can be chosen in 20 ways. So we can write number of outcomes favorable to defective pin is equal to 20. Now we know probability of getting a defective pin is equal to number of outcomes favorable to defective pin upon total number of possible outcomes. Now number of outcomes favorable to defective pin is equal to 20 and total number of possible outcomes is equal to 144. So probability of getting a defective pin is equal to 20 upon 144. Now we will cancel common factor 4 from numerator and denominator both and we get 5 upon 36. So we can write probability of getting a defective pin is equal to 5 upon 36. And we know probability of getting a defective pin is equal to probability that Noory will not buy a pin. So we can write probability that she will not buy a pin is equal to 5 upon 36. So we get probability that she will not buy a pin is equal to 5 upon 36. Note that event that she will buy a pin and event she will not buy a pin are two complementary events. And we know that sum of probabilities of complementary events is equal to 1. Now probability that she will buy a pin is equal to 31 upon 36 and probability that she will not buy a pin is equal to 5 upon 36. Now if we add these two terms we get 36 upon 36 which is further equal to 1. So we get LHS is equal to RHS. So our answer is correct. So required answer for the first part is 31 upon 36 and for second part is 5 upon 36. This completes the session. Hope you understood the solution. Take care and have a nice day.