Page 18 - Probability Demystified

CHAPTER 1 Basic Concepts 7

Rule 5: The probability that an event will not occur is equal to 1 minus the
probability that the event will occur.

For example, when a die is rolled, the sample space is 1, 2, 3, 4, 5, 6.
Now consider the event E of getting a number less than 3. This event
consists of the outcomes 1 and 2. The probability of event E is
2
1
PðEÞ¼ ¼ . The outcomes in which E will not occur are 3, 4, 5, and 6, so
6 3
2
the probability that event E will not occur is 4 ¼ . The answer can also
6 3
be found by substracting from 1, the probability that event E will occur.
1
2
That is, 1 ¼ .
3 3
If an event E consists of certain outcomes, then event E (E bar) is called the
complement of event E and consists of the outcomes in the sample space
which are not outcomes of event E. In the previous situation, the outcomes in
E are 1 and 2. Therefore, the outcomes in E are 3, 4, 5, and 6. Now rule five
can be stated mathematically as
PðEÞ¼ 1 PðEÞ:

EXAMPLE: If the chance of rain is 0.60 (60%), find the probability that it
won’t rain.

SOLUTION:

Since P(E) = 0.60 and PðEÞ¼ 1 PðEÞ, the probability that it won’t rain is
1 0.60 = 0.40 or 40%. Hence the probability that it won’t rain is 40%.

PRACTICE

1. A box contains a $1 bill, a $2 bill, a $5 bill, a $10 bill, and a $20 bill.
A person selects a bill at random. Find each probability:
a. The bill selected is a $10 bill.
b. The denomination of the bill selected is more than $2.
c. The bill selected is a $50 bill.
d. The bill selected is of an odd denomination.
e. The denomination of the bill is divisible by 5.