 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says A dice thrown again and again until three sixes are obtained Find the probability of obtaining the third six in the sixth throw of the dice So let's start the solution now according to the given question a dice thrown again and again Until three sixes are obtained So the repeated throwing are die are pernolutrials now probability of getting a six that is P is equal to one over six and the probability of not getting a six a throw That is probability of failure which is given by q is equal to 1 minus p and this is equal to 1 minus 1 over 6 which is equal to 5 over 6 Now we have to find the probability of obtaining the third six in the sixth throw of the dice So for this we will first find out the probability of two sixes in the five throws of a die Now we have the probability of x successes is equal to ncx into q raised to power n minus x into p raised to power x where x is from 0 to n and Q is equal to 1 minus p so the probability of getting two sixes in five throws of a die is given by five c2 Into q raised to power n minus x now we have q is equal to five over six So this is equal to five c2 into Five over six raised to power five minus two Into p raised to power x We have p is equal to one over six one over six raised to power two And this is equal to five c2 into five over six raised to power three Into one over six square Now we want to find the probability of obtaining the third six in the sixth throw of the die This is the probability of getting two sixes in five throws the probability of Getting a six in the sixth row is equal to one over six hence the probability of Getting a third six in the sixth throw is equal to five c2 into One over six raised to power two Into five over six raised to power three Into one over six Now this is equal to five c2 which is ten into five q over six here into six q into six and This is equal to ten into one twenty five over Forty-six thousand six hundred fifty-six and this is again equal to five into one twenty five over Twenty-three thousand three hundred twenty-eight and this is equal to six twenty five over Twenty-three thousand three hundred twenty-eight Hence the probability of obtaining the third six in the sixth throw of the die is Six twenty five over Twenty-three thousand three Hundred twenty-eight So this is the answer for the question This completes our session. I hope the solution is clear to you. Bye and have a nice day