In this lesson you will learn to reach fundamental understandings of conditional probability by modeling scenarios.

Let’s Review The 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 BagBlue Shapes Blue Triangles 84 count of blue triangles count of blue shapes count of blue triangles count of blue shapes 8 4 =

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 32 count of prime odd outcomes count of odd outcomes 3 2 =

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? F IRST S ECOND T HIRD C REW T OTAL S URVIVED D IED T OTAL

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. F EMALE M ALE T OTAL B ROWN H AIR 347 B LONDE H AIR 213 T OTAL 5510 P(Brown Hair l Female) = 5 3 P(Br Hair ∩ Female) P( Female) = =

Core Lesson What is the probability of a passenger on the Titanic surviving given they were in first class? F IRST S ECOND T HIRD C REW T OTAL S URVIVED D IED T OTAL P(Survived l First) = P(First) P(Survived ∩ First) = 64.5%

Core Lesson What is the probability of a passenger on the Titanic surviving given they were in third class? F IRST S ECOND T HIRD C REW T OTAL S URVIVED D IED T OTAL P(Survived l Third) = P(Third) P(Survived ∩ Third) = 25.2%

Core Lesson What is the probability of a passenger on the Titanic being a crew member given they survived? F IRST S ECOND T HIRD C REW T OTAL S URVIVED D IED T OTAL P(Crew l Survived) = P(Survived) P(Crew ∩ Survived) = 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(A C ∩ B C ) P(A) P(B) P(A ∩ B) = 1

Core Lesson Find 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(PT C ∩ PF C ) P(PT)P(PF) P(PT ∩ PF) P (PF l PT) = P (PT ∩ PF) P (PT) =.5= 50%

Core Lesson Find 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(C C ∩ CS C ) P(CS)P(C) P(C ∩ CS) P (CS l C) = P (C ∩ CS) P (C) = 51%=.51