 Hello and welcome to the session. In this session we discuss the following question which says like a bar graph of an experiment of tossing an ideal coin six times where the preferred outcome is head. If we suppose P to be the probability of success of an event and Q to be the probability of failure of the event in one trial and suppose there are n number of trials if the number of successes denoted by the random variable capital X is 0 that is in one trial there is no success then in that case the probability P would be given by mc0 into P to the power of 0 into Q to the power of n minus 0 which is n and this is equal to Q to the power of n and in case if the number of successes is 1 then the probability would be given by mc1 into P to the power of 1 into Q to the power of n minus 1. If number of successes is 2 then the probability is given as mc2 P to the power of 2 into Q to the power of n minus 2. If the number of successes is cr then probability is ncr into P to the power of r into Q to the power of n minus r and if the number of successes is n then probability is mcn into P to the power of n into Q to the power of n minus n that is 0 and this is equal to P to the power of n. This is the key idea that we use in this question. Let's proceed with the solution now. So in this experiment we are tossing an ideal coin 6 times so the number of trials in this case that is m would be equal to 6. Now P that is the probability of success would be the probability of getting head this would be equal to 1 upon 2 or you can say 0.5. Now Q is the probability of failure that is the probability of not getting head would be equal to 1 minus P that is 1 minus 0.5 which is again 0.5. Probability of not getting head means probability of getting a tail. Now then the following cases would arise first we would have 6 tails that is there would be no head so in this case as there is no head number of successes would be 0 and the probability would be 6C0 into P that is 0.5 to the power of 0 into Q that is 0.5 to the power of 6 minus 0 which is 6 and so this is equal to 0.5 to the power of 6 which is equal to 0.015625. Consider the next case in which we get 1 head and 5 tails. Now as there is 1 head so number of successes is 1 and so in this case the probability would be given as 6C1 into P that is 0.5 to the power of 1 into 2 that is 0.5 to the power of 6 minus 1 that is 5. So this value will come out as 0.09375. Now the next case in which we have 2 heads 4 tails in this the number of successes would be 2 as there are 2 heads and so the probability would be given by 6C2 into 0.5 that is P to the power of 2 into Q that is 0.5 to the power of 6 minus 2 that is 4 and this is equal to 0.234375. Now the next case in which we get 3 heads and 3 tails in this the number of successes is 3 so there are 3 heads and the probability would be given as 6C3 into 0.5 to the power of 3 into 0.5 to the power of 3 and this would be equal to 0.3125. Let's consider the next case in which we have 4 heads and 2 tails in this case the number of successes is 4 as there are 4 heads and so the probability would be given as 6C4 into 0.5 to the power of 4 into 0.5 to the power of 2 and so this would be equal to 0.234375. Now the next case in which there would be 5 heads and 1 tail so number of successes would be 5 as the number of heads in this case are 5 and so the probability would be given as 6C5 into 0.5 to the power of 5 into 0.5 to the power of 1 and so this would be equal to 0.09375. Now consider the case in which we get 6 heads so the number of successes is 6 here and so the probability would be 6C6 into 0.5 to the power of 6 into 0.5 to the power of 0 and so this would be equal to 0.015625. Now we will draw a bar graph using this table. Now when the number of successes that is number of heads is 0 then the probability is 0.015625. This rectangular bar shows the number of heads as 0 with probability 0.015625. Next we have if the number of heads is 1 then the probability is 0.09375. This rectangular bar shows the number of heads as 1 and having probability 0.09375 then we have if the number of heads is 2 then the probability is 0.234375. So this rectangular bar shows the number of heads as 2 and the probability is 0.234375. Now when the number of heads is 3 probability is 0.3125. So this rectangular bar indicates the number of heads as 3 and probability 0.3125. For the number of heads 4 probability is 0.234375. So this rectangular bar is indicating number of heads 4 and probability 0.234375. For the number of heads as 5 probability is 0.09375. This is the rectangular bar indicating number of heads as 5 and probability as 0.09375. Now if the number of heads is 6 then the probability is 0.015625. So this rectangular bar shows number of heads as 6 and probability as 0.015625. So this is the bar graph for the experiment of tossing an ideal coin 6 times when our preferred outcome is head. This completes the session. Hope you have understood the definition of this question.