Page 35 - Probability Demystified

24 CHAPTER 2 Sample Spaces

EXAMPLE: A coin is tossed and a die is rolled. Find the probability of
getting
a. A head on the coin and a 3 on the die.
b. A head on the coin.
c. A 4 on the die.
SOLUTION:

a. Since there are 12 outcomes in the sample space and only one way to
get a head on the coin and a three on the die,
1
PðH3Þ¼
12
b. Since there are six ways to get a head on the coin, namely H1, H2, H3,
H4, H5, and H6,
6 1
Pðhead on the coin) ¼ ¼
12 2
c. Since there are two ways to get a 4 on the die, namely H4 and T4,
2 1
Pð4 on the die) ¼ ¼
12 6

EXAMPLE: Three coins are tossed. Draw a tree diagram and find the sample
space.

SOLUTION:
Each coin can land either heads up (H) or tails up (T); therefore, the tree
diagram will consist of three parts and each part will have two branches.
See Figure 2-2.

Fig. 2-2.