Page 36 - Probability Demystified

CHAPTER 2 Sample Spaces 25

Hence the sample space is HHH, HHT, HTH, HTT, THH, THT, TTH,
TTT.
Once the sample space is found, probabilities can be computed.
EXAMPLE: Three coins are tossed. Find the probability of getting

a. Two heads and a tail in any order.
b. Three heads.
c. No heads.
d. At least two tails.
e. At most two tails.
SOLUTION:

a. There are eight outcomes in the sample space, and there are three ways
to get two heads and a tail in any order. They are HHT, HTH,
and THH; hence,
3
P(2 heads and a tail) ¼
8
b. Three heads can occur in only one way; hence
1
PðHHHÞ¼
8
c. The event of getting no heads can occur in only one way—namely
TTT; hence,
1
PðTTTÞ¼
8
d. The event of at least two tails means two tails and one head or three
tails. There are four outcomes in this event—namely TTH, THT,
HTT, and TTT; hence,
4 1
P(at least two tails) ¼ ¼
8 2
e. The event of getting at most two tails means zero tails, one tail,
or two tails. There are seven outcomes in this event—HHH, THH,
HTH, HHT, TTH, THT, and HTT; hence,
7
P(at most two tails) ¼
8
When selecting more than one object from a group of objects, it is
important to know whether or not the object selected is replaced before
drawing the second object. Consider the next two examples.