PROBABILITY
An event is a collection or set of outcomes. For example, suppose that a die with faces numbered 1, 2, 3, 4, 5, and 6 is rolled. All
the possible outcomes are 1, 2, 3, 4, 5, and 6. Let A be the event that a 1, 3, or 5 is rolled. The event A is made up of the outcomes 1,
3, and 5; that is, {A = 1, 3, 5} The event A can also be described by saying that the number is odd. A possible outcome is the
elementary building block from which events are made up. An event is a set of possible outcomes. Of course, it is possible for an
event to consist of a single possible outcome. For example, suppose that B = {4}; that is, the event B is the result that a 4 is rolled.
An event consisting of a single possible outcome is called an elementary event. Thus, B, which is {4}, is an elementary event.
However, in general, an outcome is more elementary than an event, with an event being a set of possible outcomes. For example, the
event C = {1, 2, 4, 6} consists of possible outcomes 1, 2, 4, and 6. Note that C is not an elementary event.
PROBABILITY IS UNDER 1
Probability is a part-to-whole ratio and can therefore never be greater than 1.To find the probability that a single event will occur, use the formula:
If there are 12 books on a shelf and 9 of them are mysteries, what is the probability of picking a mystery?
To find the probability that two events will both occur, find the probability that the first event occurs and multiply this by the
probability that the second event occurs given that the first event occurs.
If there are 12 books on a shelf and 9 of them are mysteries, what is the probability of picking a mystery first and a nonmystery
second if exactly two books are selected?
Probability of picking a mystery:
Probability of picking a nonmystery: (Originally there were 9 mysteries and 3 nonmysteries. After the mystery is selected, there
are 8 mysteries and 3 nonmysteries, or 11 books remaining.)
Probability of picking both books:
The probability is This probability can also be expressed as 0.75 or 75%.