1
Solution for selected problems Chapter 6
6.2
a) The probabilities for each possible outcome in the sample space are the same: 1/36. There is
only one instance in which the maximum is one; thus, the probability is 1/36. There are three
instances in which the maximum is two; thus, the probability is 3/36. Etc. For example, in the
sample space below, all cases in which the maximum roll is four are in bold. There are seven
such cases, and so the probability is 7/36.
The sample space: {(1,1),(1,2),(1,3),(
1,4
),(1,5)(1,6),(2,1),(2,2),(2,3),(
2,4
),(2,5)(2,6),(3,1),
(3,2),(3,3),(
3,4
),(3,5)(3,6),(
4,1
),(
4,2
),(
4,3
),(
4,4
),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5)(5,6),
(6,1),(6,2),(6,3),(6,4),(6,5)(6,6}
b) These probabilities satisfy the two conditions for a probability distribution: 0
≤ P(
x
)
≤ 1; and
Σ
P(x)=1
6.4
a) Final grade Probability
4 0.20
3
0.40
2
0.30
1
0.10
b)
= 1(0.10) + 2(0.30) + 3(0.40) + 4(0.20) = 2.70. The average final grade for the class is 2.7.
6.5