Question

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

Answer 1

When a coin is tossed twice, the possible outcomes are HH, HT, TH, TT.
The second throw results in a head in HH, TH.
The second throw results in a tail in HT, TT.
Now, a dice is thrown.
The possible outcomes on a dice are 1, 2, 3, 4, 5 and 6.
The sample space is given by
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.