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1. Suppose a coin having probability 0.7 of coming up heads is tossed three times. Let X denote the number of heads that appear in the three tosses. Determine the probability mass function of X. 2. Suppose three fair dice are rolled. What is the probability at most one six appears? 3. On a multiple-choice exam with three possible answers for each of the five questions, what is the probability that a student would get four or more correct answers just by guessing? 4. An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up? Solutions: 1. P(0)=(0.3)3=0.027 P(1)=3(0.3)2(0.7)=0.189 P(2)=3(0.3)(0.7)2=0.441 P(0)=(0.7)3=0.343 1 5 1 200 2. 1- 3 C 2 [ ]2 [ ] 3 C3 [ ]3 6 6 6 216 1 2 1 11 3. 5 C 4 [ ]4 [ ] 5 C5 [ ]5 3 3 3 243 4. 1-(0.95)52-52(0.95)51(0.05)