Suppose that events A and B are mutually exclusive with P(A) = ½ and p(B) = 1/3. a. Are A and B independent events? Explain how you know. b. Are A and B complementary events? Explain how you know. 34. Two fair coins are tossed. Define. A = Getting a head on the first toss B = Getting a head on the second toss A and B = Getting a head on both the first and scond tosses. A or B =
Getting a head on the first toss, or the second toss, or both tosses. a. Find P(A) = the probability of A b. Find P(b) = the probability of B c. Using the multiplication rule (rule 3b), find P(A and B) d. Using the addition rule (Rule 2a), find P(A or B) 35. In a recent election, 55% of the voters were Repulicans, and 45% were not. Of the Republicans, 80% voted for Candidate X, and of the non-Republicans, 10% voted for C
andidate X. Consider a randomly selected voter. Define A = Voter is Republican B = voted for Candidate X. a. Write values for P(A), P(Ac), P(B|A), and P(B|Ac). b. Find P(A and B), and write in words what outcome it represents. c. Find P(Ac and B), and write in words what outcome it represents. d. Using the results in parts (b) and (c), find P(B), Hint: The events in parts (b) and (c) cover all of the ways in which B can happen. e.
Use the result in part (d) to state what percent of the vote Candidate X received.
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