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### Unit 4

Example 1: Determine which events are mutually exclusive.

Section 4-3

4-3: The Addition Rules for Probability For Example: If we wanted to know the probability a student is in 9thor 10th grade, there are two possibilities to consider:

- 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

- 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

- 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?

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