The sample space {HH, HT, TH, TT} represents the possible outcomes of flipping a fair coin twice. Here's how it matches the repeated experiments listed:
1. Flipping a fair coin once: This sample space does not match flipping a coin once because it includes outcomes from two coin flips, not just one.
2. Flipping a fair coin twice: This is the correct match. The sample space {HH, HT, TH, TT} represents the outcomes of flipping a fair coin twice.
3. Spinning a spinner with 4 sections labeled 1 through 4: This sample space does not correspond to spinning a spinner with 4 sections as it represents coin flips, not spinner outcomes.
4. Rolling a number cube twice: The sample space {HH, HT, TH, TT} does not align with rolling a number cube twice as it represents coin flip outcomes, not dice rolls.
Therefore, the sample space {HH, HT, TH, TT} best represents the repeated experiment of flipping a fair coin twice.
