This document provides a lesson on conditional probability that includes: 1. Examples and formulas for calculating conditional probability 2. Practice problems solving for conditional probabilities in situations involving cards, dice, families, and committees 3. A discussion of how conditional probability can inform decisions about driving while using a cell phone, health, and sports.

1. Prepared by:
Teacher III

2. Learning Objectives
1. Illustrate conditional probability;
2. Solve problems involving conditional
probability; and
3. Cite uses of probability in real-life
situations.

3. Let’s Recall
Probability of the Union of Two Events
𝑃 𝐴 ∪ 𝐵 = 𝑃 𝐴 + 𝑃 𝐵 − 𝑃(𝐴 ∩ 𝐵)
Probability of Independent Events
𝑃 𝐴 ∩ 𝐵 = 𝑃(𝐴) ∙ 𝑃(𝐵)
Probability of Dependent Events
𝑃 𝐴 ∩ 𝐵 = 𝑃(𝐴) ∙ 𝑃(𝐵│𝐴)

4. Question 1:
When a card is drawn from the standard deck
of cards, what is the probability that it is a face
card or an ace?
4
13

5. Question 2:
When two cards are drawn from a standard
deck of cards, one a time what is the probability
that the first card is a face card and the second
card is an ace?
With replacement:
3
169
Without replacement:
4
221

6. Question 3:
When two cards are drawn from a pack of
cards, one at a time, what is the probability that
both are face cards?
With replacement:
9
169
Without replacement:
11
221

7. Situation: Mario bought four different batteries.
Of these four, one is defective. Two are to be
selected at random for use on a particular day.
1. List the sample space.
2. Find the probability that the second battery
selected is not defective.
3. What if you find the probability that the
second battery selected is not defective,
given that the first was not defective.

8. Rolling a Die
If we let 𝐴 be the event of getting an odd number and
𝐵 of getting a number greater than 3, then 𝑷 𝑨 =
𝟑
𝟔
and
𝑷 𝑩 =
𝟑
𝟔
.
Suppose that after we toss the die, we are informed
that B has occurred. That is, a face which shows more than
3 dots comes up. What is the probability of 𝐴? When 𝐵 has
occurred, the 6 possible outcomes reduce the number of
possibilities to only 3. Since one of these corresponds to the
occurrence of A, we say that the probability of getting an
odd number given a number greater than 3 has occurred is
𝟏
𝟑
. In symbols, 𝑷 𝑨 𝑩 =
𝟏
𝟑
.

9. What probability is it?
Conditional Probability is the probability that
an event will occur given that another event has
already occurred.
If 𝑨 and 𝑩 are any events, then
𝑷 𝑨 𝑩 =
𝑷(𝑨∩𝑩)
𝑷(𝑩)

10. Problem 1
The probability that Arnel studies and passes
his math test is
𝟗
𝟐𝟎
. If the probability that he
studies is
𝟒
𝟓
, what is the probability that he
passes the math test given that he has studied?
9
16

11. Problem 2
In a two-die experiment, what is the probability
that the sum of the numbers falling is 8 if it is
known that one of the numbers is 5?
2
11

12. Problem 3
Maria will randomly draw two cards in
succession from a standard deck of cards.
What is the probability that the second card is a
king given that the first card is a queen? How
about if the first card is a king?
4
51
1
17

13. Valuing
How can we use probability to make informed
decisions about any of the following:
• driving and cell phone use
• diet and health
• professional athletics

14. What I Learned
1. Conditional probability is the probability that
___________.
2. The formula for conditional probability is
___________.

15. Individual Work
1. The probability that Rose will visit the parlor
and the doctor today is
𝟑
𝟐𝟎
. If the probability
that she visits the doctor is
𝟏𝟏
𝟐𝟎
, what is the
probability that she visits the parlor, given
that she has visited the doctor?
3
11

16. 2. A family has two children. What is the
probability that the younger child is a
girl, given that at least one of the
children is a girl?
2
3
Individual Work

17. 3. You roll one six-sided die. What is the
probability of getting an even number
given you know the number is a prime
number?
1
3
Individual Work

18. Individual Work
4. In rolling two dice, what is the probability
that the sum of two numbers will be
greater than 9, given that the first die is
a 5?
1
3

19. Individual Work
5. You are playing a game of cards where
the winner is determined by drawing
two cards of the same suit. What is the
probability of drawing club on the
second draw if the first card drawn is a
club?
4
17

20. Assignment
Solve the following problems.
1. Two men and three women are in a
committee. Two of the five are to be
chosen as officers.
2. If the officers are chosen randomly, what is
the probability that both officers will be
women? What is the probability that both
officers will be women given that at least
one is a woman?