Chapter 5.2 AP Stats

addition rule for mutually exclusive (disjoint) events

The addition rule for mutually exclusive (disjoint) events A and B says that P(A or B) = P(A) + P(B) CAUTION: Note that this rule works only for mutually exclusive (disjoint) events.

complement

The complement AC contains exactly the outcomes that are not in A.

general addition rule

If A and B are any two events resulting from some chance process, the general addition rule says that P(A or B)=P(A)+P(B)-P(A and B) The probability P(A and B) that events A and B both occur is called a joint probability. If the joint probability is 0, the events are disjoint.

Addition rule for mutually exclusive events

If A and B are mutually exclusive, P(A or B)=P(A)+P(B)

disjoint

If the joint probability is 0, the events are disjoint

Complement rule

P(A^C )=1-P(A)

Rules that a valid probability model must obey:

1.If all outcomes in the sample space are equally likely, the probability that event A occurs is P(A)=(number of outcomes in event A)/(total number of outcomes in sample space) 2.The probability of any event is a number between 0 and 1. 3.All possible outcomes together must have probabilities that add up to 1. 4.The probability that an event does not occur is 1 minus the probability that the event does occur.

Venn diagram

A Venn diagram consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the chance process.

probability model

A probability model is a description of some chance process that consists of two parts: a list of all possible outcomes and the probability for each outcome.

event

An event is any collection of outcomes from some chance process

Finding Probabilities: Equally Likely Outcomes

If all outcomes in the sample space are equally likely, the probability that event A occurs can be found using the formula P(A)= (number of outcomes in event A) / (total number of outcomes in sample space)

complement rule

The complement rule says that P (AC) = 1 - P(A), where AC is the complement of event A; that is, the event that A does not occur.

intersection

The intersection of events A and B (A ∩ B) is the set of all outcomes in both events A and B.

sample space

The list of all possible outcomes is called the sample space. A sample space can be very simple or very complex

joint probability

The probability P(A and B) that events A and B both occur is called a joint probability

union

The union of events A and B (A ∪ B) is the set of all outcomes, in either event, A or B. HINT: To keep the symbols straight, remember ∪ for Union and ∩ for intersection.

mutually exclusive (disjoint)

Two events A and B are mutually exclusive (disjoint) if they have no outcomes in common and so can never occur together—that is, if P(A and B) = 0. CAUTION: Note that this rule works only for mutually exclusive (disjoint) events.

Two-Way Tables, Probability, and the General Addition Rule There are two different uses of the word or in everyday life.

When you are asked if you want "soup or salad," the waiter wants you to choose one or the other, but not both. However, when you order coffee and are asked if you want "cream or sugar," it's OK to ask for one or the other or both. In mathematics and probability, "A or B" means one or the other or both. When you're trying to find probabilities involving two events, like P(A or B), a two-way table can display the sample space in a way that makes probability calculations easier.

Basic Probability Rules

•For any event A, 0≤P(A)≤1. •If S is the sample space in a probability model, P(S)=1 •In the case of equally likely outcomes, P(A)=(number of outcomes in event A)/(total number of outcomes in sample space) •Complement rule: P(A^C )=1-P(A) •Addition rule for mutually exclusive events: If A and B are mutually exclusive, P(A or B)=P(A)+P(B)