AP Statistics Section 6.2 B Probability Rules

If A represents some event, then the probability of event A happening can be represented as _____

Probability Rules

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

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) = ____.

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” _____.

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 ___________

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: _______________.

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.

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 the probabilities 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)

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)

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)

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)

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) =