 Hi and how are you all today? My name is Priyanka. The question to be discussed is an organization selected 2400 families at random and surveyed them to determine a relationship between the income level and the number of vehicles in a family. The information gathered is listed in the table below. Now this is the table in which the monthly income are written like this and the vehicle per family 0, 1, 2 and above 2 are mentioned with respect to the income group. What we need to do is suppose a family is chosen, find the probability that the family chosen is earning rupees 10,000 to 13,000 per month and owning exactly two vehicles, earning rupees 16,000 or more per month and owning exactly one vehicle, earning less than 7,000 per month and does not own any vehicle, earning 13,000 to 16,000 per month and owning more than two vehicles and owning not more than one vehicle. Now for these five parts I need to mention the probability for each and every case but proceeding on with the solution we should be well versed with the formula that will help us in doing so. Probability of finding any event or finding the probability of any event is equal to number of possible outcomes divided by total number of outcomes. Now the knowledge of this formula is the key idea to this question. Let us proceed on with the solution. Now for the first part I need to mention that the family chosen is earning rupees 10,000 to 13,000 per month so earning rupees 10,000 to 13,000 per month exactly vehicles. So I need to find out the probability of it. Now total number of the number which comes out here will be taken from the table above. Now here between 10,000 to 13,000 and having two vehicles give you the number as 29. So the answer over here is 29. Total number of families we are talking about are 2400 right. So our required probability 29 divided by that is number of possible outcomes divided by the total number of outcomes that is 2400. Since this cannot further simplify the answer becomes 29 by 2400 and this is the answer to our first part. Now for the second part we need to tell earning rupees 16,000 or more per month and owning exactly one vehicle. So let us find out the number from above table. So here 16,000 or more and owning one vehicle so the number corresponding to 16,000 or more income group is 579. So here it is 579. We know that total number of families is fixed to be 2400. So the required probability is equal to 579 divided by 2400 and this is our required answer to the second part. Now the third part is earning less than 7,000 per month and does not own any vehicle. Now let us refer to the table again and it is less than 7,000 owning no vehicle. So the answer is 10. So the number of families which are earning less than 7,000 per month and does not own any vehicle. Again total number of families is as 2400. So the required probability is equal to 10 divided by 2400. The answer comes out to be 1 by 240. So this is the required answer to the third. The fourth part says earning rupees 13,000 to 16,000 per month and owning more than two vehicles. So looking at the table given to us are 25 such families and we know the total number of families are 2400. So the required probability is equal to 25 over 2400 that is further equal to 1 by 96 and this is the answer to the fourth part. Proceeding on with the fifth part here we need to find out the probability of the number of families not more than 1 vehicle. Right now here it will be equal to what? It will be equal to families owning zero vehicle or that is no vehicle plus families owning one vehicle. Right that will be equal to the sum of all the families owning no vehicle and one vehicle that is 10 plus 0 plus 1 plus 2 plus 1 that is the number of families owning no vehicle plus the number of families owning one vehicle and that is 160 plus 305 plus 535 plus 469 plus 579 that is equal to 14 plus 2148 that is 2162. So here the required probability is equal to that is over here sorry 2048 and here it is 2062. So a required probability is 2062 divided by 2400 and on simplifying it out we have 1031 divided by 1200. This is the required answer to the fifth and final part. Hope you enjoy have a good day and bye for now.