Page 55 - Probability Demystified

44 CHAPTER 3 The Addition Rules

Mutually Exclusive Events

Many problems in probability involve finding the probability of two or more
events. For example, when a card is selected at random from a deck, what is
the probability that the card is a king or a queen? In this case, there are two
situations to consider. They are:
1. The card selected is a king
2. The card selected is a queen
Now consider another example. When a card is selected from a deck, find
the probability that the card is a king or a diamond.
In this case, there are three situations to consider:
1. The card is a king
2. The card is a diamond
3. The card is a king and a diamond. That is, the card is the king of
diamonds.
The difference is that in the first example, a card cannot be both a king and
a queen at the same time, whereas in the second example, it is possible for the
card selected to be a king and a diamond at the same time. In the first
example, we say the two events are mutually exclusive. In the second example,
we say the two events are not mutually exclusive. Two events then are
mutually exclusive if they cannot occur at the same time. In other words, the
events have no common outcomes.

EXAMPLE: Which of these events are mutually exclusive?
a. Selecting a card at random from a deck and getting an ace or a club
b. Rolling a die and getting an odd number or a number less than 4
c. Rolling two dice and getting a sum of 7 or 11
d. Selecting a student at random who is full-time or part-time
e. Selecting a student who is a female or a junior

SOLUTION:
a. No. The ace of clubs is an outcome of both events.
b. No. One and three are common outcomes.
c. Yes
d. Yes
e. No. A female student who is a junior is a common outcome.