 Hello and welcome to the session. My name is Asha and I am going to help you with the last question of this exercise which says a die is drowned repeatedly until a six comes up. What is the sample space for this experiment? So let's start with the solution. The possible outcomes when a die is rolled are 1, 2, 3, 4, 5 and 6. Suppose this is a die which is rolled. Now when it is rolled the possible outcomes are 1, 2, 6, 1, 2, 3, 4, 5 and 6. When 6 appears we stop otherwise we again roll a die. So here again we have 6 possible outcomes of 1, 2, 3, 4, 5 and 6. Similarly if 2 appears we again roll a die. So here again the 6 possible outcomes are from 1, 2, 6. Similarly with 3 also 1, 2, 3, 4, 5 and 6 with 4 also we have 6 possible outcomes 1, 2, 3, 4, 5 and 6 and with 5 also 1, 2, 5 and 6. Now here the possible outcomes are 1, 2, 3, 4, 5 and 6. So for 6 we stop and for other numbers from 2 to 5 we again roll a die. Similarly here also for 6 we stop and for 1, 2, 3, 4 and 5 we again roll a die. Here also for 1, 2, 3, 4, 5 we roll a die and 6 we stop. Same the case here for 6 we stop and for the last case also we roll a die and for 6 we stop. So the sample space of the given experiment is for 6 we stop and for 1 we roll a die. If it comes 6 then we stop. Similarly for 2 also if it comes 6 then we stop. 3 also if it comes 6 then we stop. 4 also if it comes 6 then we stop. For 5 also if it comes 6 then we stop. It comes 1 then we again roll a die. So we have 1, 1 and we have 1, 2. Now for 1 we have 1, 5, 6. Here we stop if 6 appears the third through. Now let's see this case 2 appears then we throw a die and the possible outcomes are 1, 2, 6. If 6 appears we stop and otherwise we have 2, 1 and so on up to 2, 5, 6 and similarly for 3 also 1, 6, 3, 2, 6 and so on up to the last test. Similarly for 4 also and the last one is 5. We have 5, 1, 6 so on. 6 appears on a die then we stop. Otherwise we keep on throwing the dies. So this is the required sample space for the given problem. Hope you have understood it. Take care and have a good day.