 Hi friends, I am Purvan. Today we will work out the following question. A coin is biased so that the head is three times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails. Let us begin with the solution now. Now in the question we are given that probability of head uttering is three times as that of tail. So we have probability of head is three upon four because three times out of four we will get a head and probability of tail is one upon four because out of four times we will get tail only once. Now let X denote number of tails in two tosses. Now when two coins are tossed we get the following four outcomes that is head head, head tail, tail head or tail tail. Now since X is the number of tails in two tosses so we have X is equal to zero one or two. Now when X is equal to zero then we have probability of X is equal to. Now when X is equal to zero it means there are no tails that is both our heads. So we have probability of X is equal to three upon four into three upon four because probability of getting a head is three upon four. When X is equal to one then we have probability of X is equal to. Now when X is one then we have one head and one tail so we can have first one as head and second one as tail. Now probability of getting a head is three upon four so we have three upon four into one upon four because probability of getting a tail is one upon four or we can get first one as tail that is one upon four into three upon four that is the second one as head and this is equal to three upon sixteen plus three upon sixteen which is equal to six upon sixteen. Now when X is equal to two then we have probability of X is equal to. Now when X is two it means we get both our tails. Now probability of getting a tail is one upon four so we get one upon four into one upon four and we have this is equal to one upon sixteen. Now we will draw the probability distribution table. So this is our probability distribution table which tells us that when X is equal to zero we get probability of X as nine upon sixteen. When X is one we get probability of X as six upon sixteen and when X is equal to two we get probability of X as one upon sixteen. So this is our answer. Hope you have understood the solution. Bye and take care.