Page 79 - Probability Demystified

68 CHAPTER 4 The Multiplication Rules

ANSWERS

1. There are five ways to get a sum of 8. They are (6, 2), (2, 6), (3, 5), (5, 3),
and (4, 4). There are two ways to get a sum of 8 when one die is a 6.
Hence,
P(one die is a six and sum of 8)
P(one die is a sixjsum of 8) ¼
P(sum of 8)
2
36
¼
5
36

2 5 2 36 1
¼ ¼
36 36 36 1 5

2
¼
5
The problem can also be solved by looking at the reduced sample
space. There are two possible ways one die is a 6 and the sum of the
dice is 8. There are five ways to get a sum of 8. Hence, the probability
2
is .
5
2. There are 3 ways to get one tail: HT, TH, and TT. There is one way to
get two tails; hence, the probability of getting two tails given that one
1
of the coins is a tail is . The problem can also be solved using the
3
formula for conditional probability:
1
4
P(two tailsjgiven one coin was a tail) ¼
3
4

1 3
¼
4 4

1 4 1
¼
4 1 3

1
¼
3