The table shows all of the possible outcomes when you roll a pair of dice. The highlighted outcomes are doubles.
There are 36 possible outcomes. If the dice are fair, each
outcome is equally likely to occur. Of those 36 outcomes, 6 are doubles. You
can measure the chances of an event happening with probability.
The probability that an event will happen is between 0 and 1
inclusive.
⦁ A
probability of 0 means that the event is impossible.
⦁ A
probability of 1 means the event is certain to happen.
⦁ The
closer a probability is to 1, the more likely it is to happen.
When all possible outcomes have an equally likely chance of happening,
the outcomes are said to be random.
Example
Population Link
1. A population distribution for California is shown. If a person is chosen
at random, what is the probability that the person is age 65 or older?
Alternative Solutions :
There
are 4 million people who are age 65 or older.
The
total population is 3 + 6 + 3 + 5 + 5 + 4 + 2 + 4 or 32 million.
The
probability of choosing a person age 65 or older is 
or 12.5%.
The probability that was found in Example 1 is called the theoretical probability.
Theoretical probability is what should occur. What actually occurs
when we conduct an experiment is called the experimental probability.
Experimental probability is often used by quality-control
inspectors.
Example
Manufacturing Link
2. A quality-control inspector for Office Suppliers checked a sample of 250
marking pens and found that 14 of them were defective. Find the experimental
probability of choosing a defective pen.
Alternative Solutions :
3. If
the percent of defective pens in Example 2 is greater than 6%, production will
be stopped. Should the quality-control inspector stop production?
Alternative Solutions :
The sample
contains 5.6% defective pens. Since this is less than 6%, the quality-control
inspector should not stop production.
Another way to measure the chance of an event occurring is
with odds.
Example
4. A bag contains 6 red marbles, 3 blue marbles, and 1 yellow marble. Find
the odds of choosing a red marble.
Alternative Solutions :
There
are 6 red marbles. So, there are 6 favorable outcomes.
There
are 3 + 1 or 4 marbles that are not red. So, there are 4 unfavorable outcomes.
odds of
choosing a red marble = 6 : 4 or 3 : 2.
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