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Last updated date: 07th Dec 2023
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# A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space for this experiment.

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Hint: To solve this question we need to have a concept of probability to be more precise we need to know about the sample space which is possible outcomes. To solve the problem we will write the sample space of each throw or cases given to us, which are twice tossing of coin and once rolling of die. With the help of these two sample spaces we will be finding the sample space of individual acts and then will be merging the possible outcomes keeping the conditions in mind which are given in the problem.

Sample Space of the coin tossed twice=$\left\{ \text{HH, HT, TT, TH} \right\}$
Favourable outcome=$\left\{ \text{HT, TT} \right\}$
Sample Space of the die rolled is= $\left\{ 1,2,3,4,5,6 \right\}$
Sample Space of the experiment is =$\left\{ \text{HT, TT, HT1, TT1, HT2, TT2, HT3, TT3, HT4, TT4, HT5, TT5, HT6, TT6 } \right\}$
$\therefore$ The sample space of the above experiment is $\left\{ \text{HT, TT, HT1, TT1, HT2, TT2, HT3, TT3, HT4, TT4, HT5, TT5, HT6, TT6 } \right\}$