AP Statistics Section 6.2 B

Probability Rules

If A represents some event, then the probability of event a

happening can be represented as _____P(A)

Probability Rules

1. A probability must be a number between 0 and 1 inclusive. Thus, for any event A, ____________1P(A)0

2. The sum of the probabilities of all possible outcomes of some

“procedure” must equal ___. If S is the sample space in a probability

model, then P(S) = ____.

1

1

3. Two events are disjoint (also called mutually exclusive) if they have no

outcomes in common (i.e. the events can never occur simultaneously).

For example, rolling a pair of dice and getting a sum of seven and rolling a pair of

dice and getting doubles would be mutually exclusive events.

If A and B are disjoint, then P(A or B) = __________.

This is the addition rule for disjoint events.

In place of “or” we may also use the symbol for a “union” _____.

P(B)P(A)

Similarly, we may use the intersection symbol ______ instead

of “and” and ___ for the “empty event” (i.e.

_________________________

the event with no outcomes in it)

If two events A and B are disjoint we can write ___________BA

The probability that an event does not occur is

1-probability the event does occur.

For an event A, the event that A does not occur is called the

complement of A, written _____

The complement rule states that: _______________.

cA

)(1)P(Ac AP

Disjoint and complement are important terms for us to understand. Perhaps we can use Venn

diagrams to clarify. In each case the large rectangle represents our sample space.

Disjoint and complement are important terms for us to understand. Perhaps we can use Venn

diagrams to clarify. In each case the large rectangle represents our sample space.

A cA

Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year.

Note that each probability is between 0 and 1, and that the sum of theprobabilities is 1 because these 4 outcomes make up the sample space.

Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year.

Find: P(WS lasts 5 games)

2121.

Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year.

Find: P(WS does not last 5 games)

7879.2121.1

Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year.

Find: P(WS lasts 6 or 7 games)

6060.3737.2323.

Example: Consider the probabilities at the right for the number of games it will take to complete the World Series(WS) in any given year.

Find: P(WS lasts 8 games)

0

In the special situation where all outcomes are equally likely, we have a simple rule for assigning

probabilities to events.

If a random phenomenon has k possible outcomes that are all equally likely, then the probability of each individual outcome is _____. The probability of an event A is

P(A) =

k1

k

Ain outcomes ofnumber