1. A coin is tossed twice. If the second throw results in tail a die is thrown. Describe the sample space for this experiment.

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A coin is tossed twice.The sample space is : $S_1=\{HH, TH, HT, TT\}.$

If the second toss shows a tail $(HT,TT),$ then a die is rolled and it sample space is: $S_1=\{1,2,3,4,5,6\}.$

If the second toss shows a rail $(HH,TH)$ then there is no further action.

Hence the contained sample space is:

$S=\{HH, TH,(HT, 1), (HT, 2), (HT, 3),$

$(HT, 4), (HT, 5), (HT, 6), (TT, 1), (TT, 2),$

$(TT, 3), (TT, 4), (TT, 5), (TT, 6)\}$

The total number of elements of the sample space is 14.