 Hi friends, I am Purva and today we will work out the following question, find the probability distribution of the number of successes in two tosses of a die where a success is defined as six appears on at least one die. Let us begin with the solution now. Now let S be the sample space of the experiment of tossing two dies or you can say two tosses of a die. Then S is a set which consists of the following thirty six outcomes, one one, one two, so on up till one six, two one, two two, so on up till two six, three one, three two, so on up till three six, four one, four two, so on up till four six, five one, five two, so on up till five six, six one, six two, so on up till six six. Now we have to find the probability distribution of the number of successes in two tosses of a die where a success is defined as six appears on at least one die. So let X denote the event that six appears on at least one die. Then there are two cases, the first case is that six does not appear on any of the two dies and the second case is that six appears on at least one die. Now since X denotes the event that six appears on at least one die, so from the first case we can say that here X is equal to zero and from the second case we can say that here X is equal to one. Now when X is equal to zero that is when six does not appear on any of the two dies then the possible outcomes are one one, one two, so on up till one five, two one, two two, so on up till two five, three one, three two, so on up till three five, four one, four two, so on up till four five, five one, five two, so on up till five five. So these are the 25 possible outcomes in which six does not appear on any of the two dies. Thus we get probability of X is equal to 25 upon 36. Because out of total 36 outcomes there are 25 possible outcomes in which six does not appear on any of the two dies. Now when X is equal to one that is when six appears on at least one die then the possible outcomes are one six, two six, three six, four six, five six, six one, six two, so on up till six six that is there are 11 possible outcomes in which six appears on at least one die. So we get probability of X is equal to 11 upon 36. Because total number of outcomes are 36 out of which there are 11 possible outcomes in which six appears on at least one die. So we get probability of X is equal to 11 upon 36. So this is our probability distribution table. From this table we can clearly see that when X is equal to zero probability of X is equal to 25 upon 36 and when X is equal to one probability of X is equal to 11 upon 36. So this is our answer. Hope you have understood the solution. Bye and take care.