3.1. Events, Sample Spaces, and Probability http://www.ck12.org
Notice that each of these 4 outcomes is equally probable, namely, the probability of each is 1/4. Thus it is a classical
probability. Notice also that the total probabilities of all possible outcomes add up to one: 1/ 4 + 1 / 4 + 1 / 4 + 1 / 4 = 1
Example:
What is the probability of throwing a dice and getting either 2, 3 ,or 4?
Solution:
The sample space for a fair dice has a total of 6 possible outcomes. However, the total number of outcomes for our
case is 3 hence,
P(A) =
The number of outcomes for{ 2 , 3 , 4 }to occur
The size of the sample space=
3
6
=
1
2
=50%
So, there is a probability of 50% that we will get 2, 3 ,or 4.
Example:
Consider an experiment of tossing two coins. Assume the coins are not balanced. The design of the coins is to
produce the following probabilities shown in the table:
TABLE3.1:
Sample Space Probability
HH 4 / 9
HT 2 / 9
T H 2 / 9
T T 1 / 9Figure:Probability table for flipping two weighted coins.
What is the probability of observing exactly one head and the probability of observing at least one head?
Solution:
Notice that the simple eventsHTandT Hcontain only one head. Thus, we can easily calculate the probability of
observing exactly one head by simply adding the probabilities of the two simple events:
P=P(HT)+P(T H)
=
2
9
+
2
9
=
4
9
Similarly, the probability of observing at least one head is: