Question

List the elements of each of the following sample spaces

C.) The set of outcomes when a coin is tossed until a tail or three heads appears.

Please explain!

Answer 1

A sample space is the set of of all outcomes possible in an experiment. Let H indicate heads and T indicate tails.

The sample space of the event 'a coin is tossed until a tail or three heads appears' = {T, HT, HHT, HHH}

Explanation: If on first toss, a tail appears, the experiment is stopped and the outcome is T.
If head is the outcome, the coin is tossed again. In that case, if second toss is tail, experiment is over and HT is the event. But if second toss is also heads, experiment goes on to third toss.
On third toss, if tail occurs, experiment is over and event is HHT. On third toss, if head appears, then we have three heads and therefore, experiment is stopped and HHH is an outcome in sample space.