Answer :
A. a basketball player shoots four free throws. The sequence of hits and misses.
S= 2x2x2x2=16 outcomes
S = {HHHH, HHHM, HHMM, HMMM, MMMM, HMHH, MHHH, HHHM, MMHH, MMMH, HMMH, MHMH, MMHM, MHMM, HMHM, HHHM}
B. a basketball player shoots four free throws. The number of baskets she makes.
S = {0, 1, 2, 3, 4}
The sample space of a given experiment is the set of all possible outcomes of the experiment. It is sometimes referred to as the "universe" of outcomes. For example, if an experiment is conducted by rolling a single die, the sample space would include the six possible outcomes of 1, 2, 3, 4, 5, and 6. Sample spaces are often denoted using set notation, such as {1, 2, 3, 4, 5, 6} for the example of a die.
In a more complicated experiment, the sample space may contain multiple outcomes. For example, if a two-sided coin is flipped and a die is rolled, the sample space would include all possible combinations of the two outcomes, such as heads and a 4, tails and a 3, heads and a 1, and so on. The sample space would be denoted as {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, where H represents "heads" and T represents "tails".
Sample spaces are important in probability calculations, as they are used to calculate the probability of each outcome. For example, in the two-sided coin and die example, the probability of rolling a 4 and getting heads would be 1/12, as there is only one combination of those two outcomes out of the 12 possible outcomes in the sample space.
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