Page 46 - Probability Demystified

CHAPTER 2 Sample Spaces 35

c. There are 26 red cards and four 6s, but the 6 of hearts and the
6 of diamonds have been counted twice, so

26 þ 4 2 28 7
Pðred card or 6) ¼ ¼ ¼
52 52 13
4. There are 36 outcomes in the sample space.
a. There are six ways to get a sum of seven. They are (1, 6), (2, 5),
(3, 4), (4, 3), (5, 2) and (6, 1); hence,

6 1
P(sum of 7) ¼ ¼
36 6
b. A sum greater than 8 means a sum of 9, 10, 11, 12, so

10 5
P(sum greater than 8) ¼ ¼
36 18
c. A sum less than or equal to five means a sum of five, four, three
or two. There are ten ways to get a sum less than or equal to five;
hence,

10 5
Pðsum less than or equal to fiveÞ¼ ¼
36 18
5. There are 36 outcomes in the sample space.
a. There are 11 ways to get a 5 on one or both dice. They are
(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 6), (5, 4), (5, 3) (5, 2),
and (5, 1); hence,
11
P(5 on one or both dice) ¼
36

b. There are 0 ways to get a sum greater than 12; hence,
0
P(sum greater than 12) ¼ ¼ 0
36
The event is impossible.

c. Since all sums are less than 13 when two dice are rolled, there are
36 ways to get a sum less than 13; hence,

36
P(sum less than 13) ¼ ¼ 1
36
The event is certain.