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A fair coin is tossed three times, and the events A and B are defined as shown below. Complete parts a through d. A: {At least one tail is observed} B: {The number of tails observed is odd} . . . a. Identify the sample points in the events A, B, AUB, A", and AnB. Identify the sample points in the event A. Choose the correct answer below. O A. A:{THH, HTH, HHT, TTT} B. A:{THH, HTH, HHT, TTT, TTH, THT, HTT} O C. A:{HHH} O D. There are no sample points in the event. Identify the sample points in the event B. Choose the correct answer below. O A. B:{THH, HTH, HHT, TTT, TTH, THT, HTT} B. B:{THH, HTH, HHT, TTT} O C. B:{HHH} O D. There are no sample points in the event.Identify the sample points in the event AUB. Choose the correct answer below. O A. AUB:{HHH} B. AUB:{THH, HTH, HHT, TTT, TTH , THT, HTT} O C. AUB:{THH, HTH, HHT, TTT} O D. There are no sample points in the event. Identify the sample points in the event A". Choose the correct answer below. A. AC: (HHH} O B. AGITHH, HTH, HHT, TTT, TTH, THT, HTT} O C. AC:(TTT}b. Find P(A), P(B), P(AUB), P( A" ), and P(ANB) by summing the probabilities of the appropriate sample points. 7 . o : P(A) = 3 (Type an integer or simplified fraction.) Find P(B). 1 P(B) = 2 (Type an integer or simplified fraction.) Find P(AUB). 7 P(AUB) = 8 (Type an integer or simplified fraction.) Find P(A). 1 P(AC) =3 (Type an integer or simplified fraction.) Compare your answer to the one you obtained in part b. Choose the correct answer below. v P(AUB) calculated using the additive rule is greater than P(AUB) calculated by summing the probabilities of the sample points. The value of P(AUB) calculated using the additive rule is less than P(AUB) calculated by summing the probabilities of the sample points. Both calculations of P(AUB) produce the same result. d. Are events A and B mutually exclusive? Why? O 0w p No, events A and B are not mutually exclusive because P(ANB) # 0. Yes, events A and B are mutually exclusive because P(ANB) = 0. No, events A and B are not mutually exclusive because P(ANB) = 0. Yes, events A and B are mutually exclusive because P(ANB) # 0. The effect of guilt emotion on how a decision maker focuses on a problem was investigated in a behavioral magazine. Atotal of 176 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, students were presented with a decision problem where the stated option had predominantly negative features (spending money on repairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Suppose one of the 176 participants is selected at random. Complete parts a through c. --H| Click the icon to view the table of chosen options and emotional states. a. Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the & stated option? The probability is 0.768 . (Round to three decimal places as needed.) b. If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state? The probability is 0.432 . (Round to three decimal places as needed.) c. Are the events {repair the car} and {guilty state} independent? First find the probability that the respondent chooses the stated option (repair the car). v c. Are the events {repair the car} and {guilty state} independent? First find the probability that the respondent chooses the stated option (repair the car). The probability is 0.330 . (Round to three decimal places as needed.) Now determine whether the events {repair the car} and {guilty state} are independent. Since the probability that the respondent chooses to repair the car is | the value found in part a, the events {repair the car} and {guilty state} | independent. Assume that x is a random variable having a Poisson probability distribution with a mean of 2.6. Use the Poisson distribution table to find the following probabilities. a. P(x=9)= D (Round to three decimal places as needed.) Cognitive scientists designed an experiment to measure x, the number of times a reader's eye fixated on a single word before moving past that word. For the experiment, x was found to have a mean of 1.3. Suppose one of the readers in the experiment is randomly selected, and assume that x has a Poisson distribution. a. Find P(x=0). b. Find P(x>1). c. Find P(x