Statistics for Decision- Making in Business - Maricopa Community ...

Given two events, and , the probability that one or the other occurs is the sum of the
individual probabilities with the double-count removed once. Mathematically,
( ) ( ) ( ) ( )
Typically,
is used (called a union) to replace the word “or”, making the above equation
( ) ( ) ( ) ( )
At the beginning of this section, we addressed a coin-tossing problem that involve the
summation of the probability of heads and the probability of tails. Let‟s see why we could get
away with not subtracting away the double-count. We use the “Or” probability set-up:
( ) ( ) ( ) ( )
We already know that the first two probabilities on the right-hand side, but what is the third
probability value Let‟s analyze its meaning:
( )
Of course, it is impossible to get both heads and tails in one toss of a coin! Any impossible
outcome has a probability of 0%. That is:
So,
( )
( ) ( ) ( ) ( )
We simply “lucked-out” when this problem worked-out according to our intuition. In general,
you need only to remember the “Or” probability formula for the reasons given to solve any
problem involving the occurrence of one outcome or another.
Example 2: It is often interesting to note how political preference (Democrat or Republican)
varies within a married couple. Suppose that in a survey of
160 couples it is found that 60 of the couples agree on a
preference to vote Democrat and 40 are such that the
husband votes Democrat and the wife votes Republican. The
total number of wives that vote Democrat is 90. What is the
probability that the couple has a husband or a wife that is
Republican
Statistics for Decision-Making in Business © Milos Podmanik Page 102