6.4 Find Probabilities of Compound Events

Example 1 Find the probability of A or BFind the probability of A or BYou randomly choose a card from a standard deck of 52 playing cards.

Solutiona. Choosing a 9 or a King are mutually exclusive events.

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

spade.

KingP9P King)or P(9

________________

452

452

________

852 ________

213

6.4 Find Probabilities of Compound Events

Example 1 Find the probability of A or BFind the probability of A or BYou randomly choose a card from a standard deck of 52 playing cards.

Solutionb. Because there is an Ace of spades, choosing an Ace or

spade are ___________________. There are 4 Aces, 13 spades, and 1 Ace of spades.

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

spade.

spade and AcePspadePAceP spade)or P(Ace

________________________

452

1352 ________

152 ________

1652 13

4

overlapping events

6.4 Find Probabilities of Compound Events

Example 2 Find the probability of A and BFind the probability of A and BYou roll two number cubes. What is the probability that you roll a 1 first and a 2 second?

Solution

________ 2) and P(1

________________

16

16 ________

136

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

independent

P(1) P(2)

6.4 Find Probabilities of Compound Events

Example 3 Find the probability of A and BFind the probability of A and BMarkers 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?SolutionBecause 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

3

10

conditional probability

6.4 Find Probabilities of Compound Events

Example 3 Find the probability of A and BFind the probability of A and BMarkers 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

___________________ blue) then and P(blue

________________

3

11

210 ________

355

P(blue) P(blue given blue)

6.4 Find Probabilities of Compound Events

Checkpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. 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.

spade) aor diamonds of P(King P(spade) diamonds) of P(King

152

13

52

14

52

7

26

6.4 Find Probabilities of Compound Events

Checkpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. 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.

orange) then and P(blue P(blue) + P(orange given blue)

315

4

14 5

1

7

2

35

17

6.4 Find Probabilities of Compound Events

Pg. 369, 6.4 #1-11