Question

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.

Answer 1

In this experiment, a coin is tossed and if the outcome is tail then a die is tossed once.

Otherwise, the coin is tossed again.

The possible outcome for coin is either head or tail.

The possible outcome for die is 1, 2, 3, 4, 5, 6

If the outcomes 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)}

Therefore the required sample space is

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