 Hi friends, I am Purva and today we will discuss the following question. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X? Let us begin with the solution now. Now, let S be the sample space of the experiment of tossing a coin 6 times. Then S is a set which consists of the following outcomes. That is when we toss a coin 6 times, then all 6 times we get head. That is we get 6 heads and 0 tails. The second outcome could be 5 heads and 1 tail. That is when we toss a coin 6 times, then 5 out of 6 times we get head and 1 time we get tail. Now the third outcome could be 4 heads and 2 tails. That is 4 out of 6 times we get heads and 2 times we get tail. Now the next outcome could be 3 heads and 3 tails. That is when we toss a coin 6 times, then 3 times we get head and 3 times we get tail. We can also get 2 heads and 4 tails. That is 2 out of 6 times we get head and 4 times we get tail. The next outcome which we can get is 1 head and 5 tails. That is when we toss a coin 6 times, then only 1 time we get head and 5 times we get tail. And the final outcome that we can get is 6 tails. That is when we toss a coin 6 times, all the time we get tail and 0 heads. Now in the question we are given that X represents the difference between the number of heads and number of tails obtained when a coin is tossed 6 times. So we have X represents difference in number of heads and tails. Now for each case above, in this sample space we get, now for this first outcome that is 6 heads we get X is equal to 6 minus 0 as X represents difference in number of heads and tails. And here we have 6 heads and 0 tails. So we get X is equal to 6 minus 0 which is equal to 6. The second outcome is 5 heads and 1 tails. So we get X is equal to 5 minus 1 which is equal to 4. The third outcome is 4 heads and 2 tails. So we get X is equal to 4 minus 2 and we get this is equal to 2. The next outcome is 3 heads and 3 tails. So we get X is equal to 3 minus 3 and we get this is equal to 0. The next outcome is 2 heads and 4 tails. So we get X is equal to 4 minus 2 which is equal to 2. Now the next outcome is 1 head and 5 tails. So we get X is equal to 5 minus 1 which is equal to 4. And the final outcome is 6 tails that is 6 tails and 0 heads. So we get X is equal to 6 minus 0 which is equal to 6. Now we have to find the possible values of X. So from here we can clearly see that the possible values of X are 6, 4, 2 and 0. As X is equal to 2, X is equal to 4 and X is equal to 6 are being repeated. So we write them only once. Thus we write our answer as X can take values 6, 4, 2 and 0. Hope you have understood the solution. Bye and take care.