Two candidates for a sample space, $S_{1}$ and $S_{2}$, are proposed. $S_{1}=\{H H, H T, T H, T T\}$, and $\mathrm{S}_{2}=\{\mathrm{HH}, \mathrm{TT}$, one $\mathrm{H}$ and one $\mathrm{T}\}$. Is $\mathrm{S}_{1}$ acceptable? Is $\mathrm{S}_{2}$ acceptable?
A) Both $S_{1}$ and $S_{2}$ are acceptable.
B) Only $S_{1}$ is acceptable.
C) Neither $S_{1}$ nor $S_{2}$ is acceptable.
D) Only $S_{2}$ is acceptable.

Question

Quizplus · Accepted Answer

Both $S_{1}$ and $S_{2}$ are acceptable because they both satisfy the definition of a sample space. A sample space is a set of all possible outcomes of an experiment. In this case, the experiment is flipping two coins. The sample space $S_{1}$ contains all four possible outcomes of flipping two coins: HH, HT, TH, and TT. The sample space $S_{2}$ contains only two of the possible outcomes of flipping two coins: HH and TT. However, this is still a valid sample space because it contains all of the possible outcomes of the experiment that are of interest to us.

Two Candidates for a Sample Space S1S_{1}S1​ And S2S_{2}S2​ , Are Proposed S1={HH,HT,TH,TT}S_{1}=\{H H, H T, T H, T T\}S1​={HH,HT,TH,TT}

Two Candidates for a Sample Space $S_{1}$ And $S_{2}$ , Are Proposed $S_{1}=\{H H, H T, T H, T T\}$