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