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)