 Good morning friends, I am Purva and today we will discuss the following question. Find the probability distribution of number of tails in the simultaneous tosses of three coins. Let us begin with the solution now. Now let S be the sample space of the experiment. Then S is a set consisting of eight outcomes. That is head-head tail, head-tail-head, tail-head-head, tail-head-tail, tail-tail-tail, head-tail-tail, head-head-head and tail-tail-head. Here we have H represents head and T represents tail. Now we have to find the probability distribution of number of tails in the simultaneous tosses of three coins. So let X denote number of tails in the simultaneous tosses of three coins. Then we have X can be 0, 1, 2 or 3. That is maximum number of tails in the simultaneous tosses of three coins is 3. That is when all of them are tails and the minimum number of tails is 0. That is when all of them are heads. Now when X is equal to 0, then we have probability of X as 1 upon 8. Because X is equal to 0 means there is no tail and that is all our heads and there is only one outcome head-head-head out of these eight outcomes which satisfies this condition. So we get probability of X as 1 upon 8. Now when X is equal to 1, then we have probability of X as X is equal to 1 means number of tails in the simultaneous tosses of three coins is 1. So these are the three outcomes which satisfies this condition. So we get probability of X as 3 upon 8 when X is equal to 2. That is number of tails in the simultaneous tosses of three coins is 2. Then we get probability of X as 3 upon 8. Because these are the three outcomes out of the eight outcomes which have two heads and one tail in the simultaneous tosses of three coins. Now when X is equal to 3, then we have probability of X as 1 upon 8. X is equal to 3 means all our tails and there is only one outcome out of these eight outcomes which satisfies this condition. So we get probability of X as 1 upon 8. Now we will draw the probability distribution table. So this is our probability distribution table which gives the probability distribution of number of tails in the simultaneous tosses of three coins. So this is our answer. Hope you have understood the solution. Bye and take care.