Probability
Probability refers to the likelihood that a given event will occur. To calculate the
probability of a single event, use the following formula:
probability = desired outcomestotal outcomes
The formula is illustrated in the following example.A certain jar has 3 red marbles, 5 black marbles, and 7 white marbles. If a
marble is to be selected at random from the jar, what is the probability that a
black marble will be selected?A (^15)
B (^13)
C 157
D 158
E (^45)
SOLUTION: In the example, an “outcome” is considered the event of selecting a
marble. Since there are 15 marbles to select, there are 15 total outcomes. The
“desired outcomes” refers to the number of events that satisfy the outcome
you want. Since there are 5 black marbles, there are five “desired outcomes.”
Using the formula, the probability of selecting a black marble is thus: desired
outcomes/total outcomes = 155 =^13.
Mutually Exclusive Events
Imagine hearing that there is a 0.6 chance of rain. What would be the chance that
it will not rain? 0.4. Why? Because the two events are mutually exclusive. Either it
will rain or it won’t, so the probability of the events must add up to 1. This example
highlights the following rule: when events are mutually exclusive, the sum of their
probabilities is 1.
For this question, write your answer in the box.
A certain event has two possible outcomes, a and b. If the probability of a
is p 3 , and the probability of b is p 5 , what is the value of p?
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 355
04-GRE-Test-2018_313-462.indd 355 12/05/17 12:04 pm