 Hi and welcome to the session. Let's work on this problem which says an experiment consists of rolling a die and Then tossing a coin once if the number on the dies even and if the number on the dies odd then a coin is tossed twice write the sample space For this experiment So let's start with the solution and The possible outcomes when a coin is tossed are head Let us denote it by edge and Tail Noting it by T and The possible outcomes when a die is rolled one two three four five and six Now here we are given That a die is rolled first So suppose This is the required die Which is rolled Then the possible outcomes are one two three four five and six Now the question further says a coin is tossed if an even number Turns up on the die So even numbers are two four now A coin is tossed so the possible outcomes are head or tail and all the three cases and F The number which appears on the dies odd then the coin is tossed twice So if one appears Then the coin is tossed twice That is there are four possible outcomes either head head head tail tail head or tail tail similarly When three appears the coin is tossed twice So again the same four possible outcomes head head head tail tail head and tail tail And when five appears Then the same four possible outcomes Head head head tail tail head and tail tail now, let's write down the Sample space for the given experiment the sample point is one H H Then we have one HT Then one TH Then one TT Then with two we have H and T So two H and 2t Then with three we have first H H 3 HD 3 TH and 3 TT and the 4 we have H and T 5 H H 5 HD 5 TH 5 TT and with six we have H and 6T So this is the required sample space for the given experiment Hope you have understood it. Take care and have a good day