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# Unit 4 - PowerPoint PPT Presentation

Unit 4. Section 4-3. 4-3: The Addition Rules for Probability . Probabilities often occur that involve two or more events. For Example : If we wanted to know the probability a student is in 9 th grade or female, there are three possibilities to consider: The student is in 9 th grade

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### Unit 4

Section 4-3

• Probabilities often occur that involve two or more events.

• For Example: If we wanted to know the probability a student is in 9th grade or female, there are three possibilities to consider:

• The student is in 9th grade

• The student is female

• The student is in 9th grade and female

• For Example: If we wanted to know the probability a student is in 9thor 10th grade, there are two possibilities to consider:

• The student is in 9th grade

• The student is in 10th grade

• Mutually exclusive events – two events that cannot occur at the same time

• Means that they have no common outcomes

• EX: rolling a 4 or a 6

• Example 1: Determine which events are mutually exclusive.

• Rolling an odd number or an even number

• Rolling a 3 or an odd number

• Rolling an odd number or a number less than 4.

• Rolling a number greater than 4 or a number less than 4.

• Example 2: Determine which events are mutually exclusive.

• Drawing a 7 or a jack

• Drawing a club or a king

• Drawing a face card or an ace

• Drawing a face card or a spade

Probability: Mutually Exclusive Events

• When two events A and B are mutually exclusive, the probability that A or B will occur is:

P(A or B) = P(A) + P(B)

• Example 3: A box contains 3 glazed doughnuts, 4 jelly doughnuts, and 5 chocolate doughnuts. If a person selects a doughnut at random, find the probability they will select a glazed or chocolate doughnut.

• Example 4:

• A) At a political rally, there are 20 Republicans, 13 Democrats, and 6 Independents. If a person is selected at random, find the probability that he or she is either a Democrat or and Independent.

• B) A day of the week is selected at random. Find the probability that it is a weekend day.

Probability: NOT Mutually Exclusive Events

• When two events A and B are NOT mutually exclusive, the probability that A or B will occur is:

P(A or B) = P(A) + P(B) – P(A and B)

• Example 5: A single card is drawn from a deck. Find the probability that it is a king or a club.

• Example 6:

• A) In a hospital unit there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are female. If a staff person is selected, find the probability that the subject is a nurse or a male.

• B) On New Year’s Eve, the probability of a person driving while intoxicated is 0.32, the probability of a person having a driving accident is 0.09, and the probability of a person having a driving accident while intoxicated is 0.06. What is the probability of a person driving while intoxicated or having a driving accident?

Homework:

• Pg 193-194: 1 – 10