 Hello and how are you all today? The question says the coin is biased so that the head is three times as likely to occur as a tail. If the coin is tossed twice find the probability distribution for the number of tails. So let us discuss the question Here it is given that when a coin is thrown The probability of getting a head is three times that of the tails. Now the coin is tossed twice therefore probability of getting a head will be equal to 3 by 4 and probability of getting the tail will be equal to 1 by 4 right now let X be the random variable which denotes the number of tails and X can take the values of 0, 1 and 2 right? so probability When X is equal to 0 this means that probability of getting no tail is equal to probability of getting head two times that will be equal to 3 by 4 that is probability of getting head into probability of getting head that is equal to 9 by 16 Now in the same manner we will be finding out probability when X is equal to 1 that means probability of getting one tail It is probability of getting a head first and then tail or or tail coming first and then head that is equal to 3 by 4 into 1 by 4 for the first case plus 1 by 4 into 3 by 4 That is equal to 3 by 16 plus 3 by 16 That is further equal to 6 by 16 Now see probability when X is equal to 2 That is probability of getting two tails That will be 1 by 4 into 1 by 4 giving us the answer as 1 by 16 therefore the required probability distribution table is When X is 0 then probability of X comes out to be 9 by 16 and probability is 1 then the answer is 3 by 8 after simplification when the probability of X is 1 by 16 that means tail is coming twice this is The required answer to the question so hope you understood whole solution well and enjoyed it too. Have a nice day ahead