In this lesson you will learn to reach fundamental

understandings of conditional probability by modeling

scenarios.

Let’s ReviewThe formula for the Conditional Probability of an event can be derived from Multiplication Rule 2 as follows:                                                                                                                                                                                                                                

Let’s Review

P (B l A) = P (A and B)

P (A)

Conditional probability – the probability of an event (B) occurring given that an event (A) has

already occurred.

Core Lesson

Ms. Rizzo has a bag of 13 red and blue triangles and circles. What is the probability a

shape is a triangle given that it is blue? Original Bag Blue Shapes Blue Triangles

8 4count of blue triangles

count of blue shapes

count of blue triangles

count of blue shapes84 =

Core Lesson

You roll a single six-sided die. The number you roll is not revealed, but you are told the outcome is an odd number. What is the probability the outcome is also prime?

count of prime odd outcomes

count of odd outcomes

All Outcomes Odd Outcomes Odd & Prime Outcomes

3 2count of prime odd outcomes

count of odd outcomes32

=

Core Lesson

count of prime odd outcomes

count of odd outcomes

count of blue triangles

count of blue shapes

Problem 1

Problem 2

P (∆ l Bl) = P (Bl ∩ ∆)

P (Bl)

P (Pr l Odd) = P (Pr ∩ Odd)

P (Odd)

In this lesson you will learn how to calculate conditional probabilities by using a two-

way table.

How do you find the probability of a passenger on the Titanic surviving given

they were in first class?... Third class?

FIRST SECOND THIRD CREW TOTAL

SURVIVED 203 118 178 212 711

DIED 122 167 528 673 1490

TOTAL 325 285 706 885 2201

Let’s Review

Conditional probability – the probability of an event (B) occurring given that an event (A) has

already occurred.

P (B l A) = P (A and B)

P (A)

Core Lesson

Finding the conditional probability from a two-way table is a simple process.

FEMALE MALE TOTAL

BROWN HAIR 3 4 7

BLONDE HAIR 2 1 3

TOTAL 5 5 10

P(Brown Hair l Female) =5

3P(Br Hair ∩ Female)

P( Female)==

Core Lesson

What is the probability of a passenger on the Titanic surviving given they were in first class?

FIRST SECOND THIRD CREW TOTAL

SURVIVED 203 118 178 212 711

DIED 122 167 528 673 1490

TOTAL 325 285 706 885 2201

P(Survived l First) =P(First)

P(Survived ∩ First)

325

203= 64.5%

Core Lesson

What is the probability of a passenger on the Titanic surviving given they were in third class?

FIRST SECOND THIRD CREW TOTAL

SURVIVED 203 118 178 212 711

DIED 122 167 528 673 1490

TOTAL 325 285 706 885 2201

P(Survived l Third) =P(Third)

P(Survived ∩ Third)

706

178= 25.2%

Core Lesson

What is the probability of a passenger on the Titanic being a crew member given they survived?

FIRST SECOND THIRD CREW TOTAL

SURVIVED 203 118 178 212 711

DIED 122 167 528 673 1490

TOTAL 325 285 706 885 2201

P(Crew l Survived) =P(Survived)

P(Crew ∩ Survived)

711

212= 29.8%

In this lesson you will learn how to calculate conditional probabilities by using a Venn

Diagram.

How do you solve this with a Venn Diagram?

A statistics professor gave her class two tests, one on Thursday and one on Friday. 31% of students passed

both tests, while 62% of students passed the Thursday test. What percent of students passing the Thursday test

also passed the Friday test?

X✓

Let’s Review

Conditional Probability Formula:

P (B l A) =

P (A and B)

P (A)

Core Lesson Venn Diagram

P(AC∩BC)

P(A) P(B)

P(A

∩B

)

= 1

Core LessonFind the probability using a Venn

Diagram.

A statistics professor gave her class two tests, one on Thursday and one on Friday. 31% of students passed both tests, while 62% of students passed the Thursday test. What percent of students passing the Thursday test also passed the Friday test?

P(PTC∩PFC)

P(PT) P(PF)

P(P

T∩

PF)

.31.62 P (PF l PT) = P (PT ∩ PF)

P (PT)

.31

.62= .5= 50%

Core LessonFind the probability using a Venn

Diagram.

The employees in the cafeteria are clearing out the shelves. Some students will get cookies with their lunch, and some students will receive cheese sticks. 23% of students will get cookies and cheese sticks. 45% of students will receive cookies. What percent of students who get cookies will also receive cheese sticks?

P(CC∩CSC)

P(CS) P(C)

P(C

∩C

S)

.23 .45 P (CS l C) = P (C ∩ CS)

P (C)

.23

.45= 51%= .51