STATISTICS Chapter 1:Independent and

Dependent Events

INDEPENDENT EVENTS

WHAT IS IN A WORD? What is dependent?

Any real-life examples?Any math examples?

What is independent?Any real-life examples?Any math examples?

VENN DIAGRAMS A graphic organizer that shows a visual

representation for all possible outcomes of an experiment and the events of the experiment in ovals.Can you draw one?Can you create an example and name the

sample space?

INDEPENDENT EVENTS Independent events are those events

which do not depend on each other.Can you think of some examples?

Choosing an ace from a deck of cards and rolling a 6 on a dice.

In a Venn-diagram independent events are represented as those events that occur in both sets.

SYMBOLS Two main symbols used with Venn-

diagrams:U = union or the outcome is in either of two

setsn = intersection or the outcome is in both

sets

Example:What is P U Q?

What is P n Q?

MULTIPLICATION RULE Used to find the probability of two

events occurring.

Examples: What is the probability of tossing two coins and

them both landing on heads?

What is the probability of tossing two coins and one landing on heads, the other on tails?

EXAMPLES Suppose 1 student is chosen at random:

What is the probability that the student is female?

What is the probability that the student is going to university?

Suppose 2 students are chosen at random, assume it is not possible to choose the same studentWhat is the probability that the first person

chooses a student who is female and the second person chooses a student who is going to a university?

Gender

University

Community College

Total

Males 28 56 84

Females

43 37 80

Total 71 93 164

DEPENDENT EVENTS

DEPENDENT EVENTS Dependent events are those events

which the probability of the second event occurring is affected by the first event occurring. Can you think of some examples?

Dependent events usually are classified with the words “without replacement”

MULTIPLICATION RULE Used to find the probability of two

events occurring.

Examples: What is the probability of choosing a seven out

of a deck of cards, then choosing another seven out of a deck of cards without replacement?

What is the probability of choosing a seven followed by another seven out of a deck of cards, with replacement?

EXAMPLE A box contains 5 red marbles and 5

purple marbles. What is the probability of drawing 2 purple

marbles followed by 1 marble in succession without replacement?

MUTUALLY INCLUSIVE AND MUTUALLY EXCLUSIVE

EVENTS

MORE TERMS AND (n) – same thing as intersection

the outcome is in both sets

OR (U) – same thing as unionoutcome is in either of two sets

MUTUALLY EXCLUSIVE EVENTS To be mutually exclusive events, two

events cannot occur at the same time.They can have no common outcomes

Can you think of some mutually exclusive events? Example: Picking a number between 1 and 10

that is both even and odd.

VENN DIAGRAM Example:

What is P(A or B)? P(A or B) = P(A) + P(B) OR means union, what is in either of the two sets

What is P(A and B) P(A and B) = overlap AND means intersection, what is common in

both

MUTUALLY INCLUSIVE EVENTS To be mutually inclusive events, two

events can occur at the same time.

Can you think of some mutually inclusive events? Picking a number from 1 to 10 that is less than 4

and picking an even number.

ADDITION PRINCIPLE Use the addition principle when finding

the probability of mutually inclusive events.P(A U B) = P(A) + P(B) – P(A n B)P(A n B) = 0 for mutually exclusive events

EXAMPLE What is the probability of choosing a

card from a deck of cards that is a club or a ten?

EXAMPLE What is the probability of choosing a

number from 1 to 10 that is less than 5 or odd?

EXAMPLE 2 fair dice are rolled. What is the

probability of getting a sum less than 7 or a sum less than 4?

THE REAL QUESTION… Are there any questions?