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6.4. Find Probabilities of Compound Events. Find the probability of A or B. Example 1. You randomly choose a card from a standard deck of 52 playing cards. Find the probability that you choose a 9 or a King. Find the probability that you choose an Ace or a spade. Solution.

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slide1

6.4

Find Probabilities of Compound Events

Find the probability of A or B

Example 1

You randomly choose a card from a standard deck of 52 playing cards.

  • Find the probability that you choose a 9 or a King.
  • Find the probability that you choose an Ace or a spade.

Solution

  • Choosing a 9 or a King are mutually exclusive events.
slide2

6.4

Find Probabilities of Compound Events

Find the probability of A or B

Example 1

You randomly choose a card from a standard deck of 52 playing cards.

  • Find the probability that you choose a 9 or a King.
  • Find the probability that you choose an Ace or a spade.

Solution

  • Because there is an Ace of spades, choosing an Ace or spade are ___________________. There are 4 Aces, 13 spades, and 1 Ace of spades.

overlapping events

slide3

6.4

Find Probabilities of Compound Events

Find the probability of A and B

Example 2

You roll two number cubes. What is the probability that you roll a 1 first and a 2 second?

Solution

independent

The events are _____________. The number on one number cube does not affect the other.

P(2)

P(1)

slide4

6.4

Find Probabilities of Compound Events

Find the probability of A and B

Example 3

Markers A box contains 8 red markers and 3 blue markers. You choose one marker at random, do not replace it, then choose a second marker at random. What is the probability that both markers are blue?

Solution

Because you do not replace the first marker, the events are __________. Before you choose a marker, there are 11 markers, 3 of them are blue. After you choose a blue marker, there are 10 markers left and two of them are blue. So, the ______________________ that the second marker is blue given that the first marker is blue, is

dependent

conditional probability

3

10

slide5

6.4

Find Probabilities of Compound Events

Find the probability of A and B

Example 3

Markers A box contains 8 red markers and 3 blue markers. You choose one marker at random, do not replace it, then choose a second marker at random. What is the probability that both markers are blue?

Solution

P(blue)

P(blue given blue)

slide6

6.4

Find Probabilities of Compound Events

Checkpoint. Complete the following exercises.

  • In a standard deck of cards, find the probability you randomly select a King of diamonds or a spade.

Choosing a King of diamonds or a spade are mutually exclusive events.

slide7

6.4

Find Probabilities of Compound Events

Checkpoint. Complete the following exercises.

  • In Example 3, suppose there are also 4 orange markers in the box. Calculate the probability of selecting a blue marker and then an orange marker, without replacement.

P(blue)

+ P(orange given blue)

slide8

6.4

Find Probabilities of Compound Events

Pg. 369, 6.4 #1-11