An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

In the given experiment, coin is tossed and if the outcome is tail then, die will be rolled.

The possible outcomes for coin are 2 = {H, T}

And, the possible outcome for die is 6 = {1, 2, 3, 4, 5, 6}

If the outcome for the coin is tail then sample space is S1= {(T, 1) (T, 2)(T, 3)(T, 4)(T, 5)(T, 6)}

If the outcome is head then the sample space is S2= {(H, H) (H, T)}

So, the required outcome sample space is S=S1S2

S= {(T, 1) (T, 2)(T, 3)(T, 4)(T, 5)(T, 6)(H, H)(H, T)}

Hence, The sample space for the given experiment.