Question

State the sample space and n(S) for the following random experiment.

A coin is tossed twice. If a second throw results in head, a die thrown, otherwise a coin is tossed.

Answer 1

When a coin is tossed twice, the outcomes are HH, HT, TH, TT.
Let A be the event that second throw results in the head when a coin is tossed twice followed by a die is thrown.
∴ A = {HH1, HH2, HH3, HH4, HH5, HH6, TH1, TH2, TH3, TH4, TH5, TH6}
The remaining outcomes i.e., HT, TT are followed by the tossing of a coin.
Let us consider this as event B.
∴ B = {HTT, HTH, TTT, TTH}
The sample space S of the experiment is A ∪ B.
∴ S = {HH1, HH2, HH3, HH4, HH5, HH6, TH1, TH2, TH3, TH4, TH5, TH6, HTH, HTT, TTH, TTH}
∴ n(S) = 16