 Hello and welcome to the session. My name is Asha and I am going to help you with the following question that says, a coin is tossed if the outcome is hit, a die is thrown. If the die shows up in even number, the die is thrown again. What is the sample space for this experiment? Let's now start with the solution. And when a coin is tossed, possible outcomes are either hit or tail. Let us denote the head by itch and tail by t. When a die is rolled, the possible outcomes are 1, 2, 3, 4, 5 and 6. Now let us see the question it says, a coin is tossed, suppose this is a coin, it is tossed then either a head will come or a tail will come, right? Now it further says if the outcome is hit, a die is thrown and if the die shows up in even number, the die is thrown again. Now when the head appears, when a die is thrown, so here the possible outcomes of the die are 1, 2, 3, 4, 5 and 6. Now when the even number turns up, then a die is thrown again. So the even numbers are 2, 4 and 6. So again a die is rolled. So when 2 appears, then a die is thrown again. That is we have 1, 2, 3, 4, 5 and 6. Also when 4 appears again a die is thrown. So here again we have 6 possible outcomes of this die. And when 6 appears, this time also a die is thrown. So again here this die has 6 possible outcomes 1, 2, 3, 4, 5 and 6. Now let us write down the sample space for this experiment. The sample point is T, then H1, H3 and H5. Now H21, H22, H23, H24, H25, H26. Since when the head turns up, then a die is rolled and if an even number appears on the die, then again a die is thrown. So we have H22, then from 1 to 6. That is H21, H22, H23, H24, H25 and H26. Now we have H41, H42, H43, H45 and H56. Since 4 is also an even number and if an even number appears on the second row of the dies, then again 1 dies is thrown. So we have H41, H42, H43, H44, H45, H46. Then we have H61, H62, H63, H64, H65, H66, H61, H62, H63, H64, H65 and H66. There are 22 sample points in the sample space. So this completes the session. Hope you have understood it well. Take care and have a good day.