Probability of Mutually Exclusive Events

Mutually exclusive events

Lesson Objective:

IDENTIFY MUTUALLY EXCLUSIVE EVENTS

CALCULATE PROBABILITIES

Outcomes are mutually exclusive if they cannot happen at the same time

Example: rolling dice once and getting 6 and 2

Multiple Choice

1. When rolling a single die, the events of rolling an even number and rolling a ‘5’ are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

3. When rolling a single die, the events of rolling an even and an odd number are ...

• Mutually Exclusive

• Not Mutually Exclusive

Multiple Choice

4. If a spinner is numbered 1 – 8, when you spin it the events of spinning an even number and a number less than 4 are ...

• Mutually Exclusive

• Not Mutually Exclusive

The Addition Rule of Probability

Mutually Exclusive Events (Disjoint)

Fill in the Blank

Show the work to find the probability of randomly selecting a non-smoker or light smoker.

Fill in the Blank

Show the work to find the probability of randomly selecting a non-smoker or a heavy smoker.

Fill in the Blank

Show the work to find the probability of selecting a student whose favorite color is red or black.

The Addition Rule of Probability

Not Mutually Exclusive Events (Not Disjoint)

More complicated OR

• To the right you see cards that can each be described in two ways

• Jack, Queen, King or Ace

• Heart, Club, Diamond or Spade

• So, one card can be two things at once, for example a Queen and a Heart.

More complicated OR

• When we talk about OR probabilities we have to take "double identity" into account

• P(Queen or Heart) seems simple... just add the Queen probability to the Heart probability.... BUT

• What about the Queen of Hearts? It will get counted twice, so....

• We will have to consider OR and take away AND to get rid of the double count

More complicated OR

• P(A or B) = P(A) + P(B) - P(AB)

• P( Queen OR Heart) = P(Queen) + P(Heart) - P(Queen of Hearts)

• P(Queen or Heart) = 4/16 + 4/16 - 1/16

• P(Queen or Heart) = 7/16

• In this simple example we can count the cards shown to see this is true!

Fill in the Blank

A sample of 100 wood and 100 graphite tennis rackets are taken from the warehouse. If 7 wood and 14 graphite are defective, show the work to find the probability that the racket is wood or defective.

Fill in the Blank

A spinner has equal regions numbered 1 through 15. Show the work to find the probability that the spinner will stop on an even number or a multiple of 3?

Fill in the Blank

Show the work to find the probability of selecting a student that is a boy or whose favorite color is blue.

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a 5 or a diamond?

• 2/52
• 4/52
• 16/52
• 26/52

Multiple Choice

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8
• 4/9 + 2/8 - 4/8
• 4/8 + 6/8 + 2/8
• 2/8 + 4/8 - 4/8

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

(Looking at the picture might help you think about this)

• 1/3

• 2/3

• 1/2

• 1/6

Multiple Choice

The enrollment at Southburg High School is 1400. Suppose 550 students take French, 700 take algebra, and 400 take both French and algebra. What is the probability that a student selected randomly takes French or algebra?

(French + Algebra - Both?)

• 1250/1400

• 700/1400

• 550/1400

• 17/28

Fill in the Blank

Show the work to find the probability of randomly selecting a man or a light smoker.

Fill in the Blank

Show the work to find the probability of randomly selecting a non-smoker or a woman.