Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event A^c and what is the probability of this event? A) A^c = {TTT, HHH, HTH}; P(A^c) = 0.375 B) A^c = {TTT, THH, HHH, HHT}; P(A^c) = 0.500 C) A^c = {TTT, HHH, HHT, HTH, HTT}; P(A^c) = 0.625 D) A^c = {TTT, HHT, HTH, THH, HHH}; P(A^c) = 0.625

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Quizplus · Accepted Answer

To find the event A^c, we need to look for the outcomes that have at least one head and one tail. So, we can exclude TTT and HHH since they both consist of only one outcome (all heads or all tails). We can also exclude HTT since it has two tails and only one head. That leaves us with HHT, HTH, and THH as the outcomes that satisfy the condition. So, A^c = {HHT, HTH, THH}. The probability of this event can be found by adding up the probabilities of these three outcomes: P(HHT) + P(HTH) + P(THH) = (1/8) + (1/8) + (1/8) = 3/8 = 0.375. Therefore, the best choice is D.

Given an Experiment in Which a Fair Coin Is Tossed