Good morning! August 16, 2017

Bellringer: 𝟏𝟐 𝟏𝟕 ÷ 𝟒 𝟑𝟒 = 𝟏𝟏 𝟏𝟐 ÷ 𝟏𝟏 𝟏𝟔 =

Standard: MGSE9-12.S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is the conditional probability of A given B is the same as the probability of A and the conditional probability of B given A is the same as the probability of B. MGSE9-12.S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, use collected data from a random sample of students in you school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. Learning Target: I CAN construct and interpret two way tables. I CAN calculate conditional probabilities and interpret the answers in context of the problem.

Conditional Probability and Two- Way Tables

Let's review the rules of Probability Lesson 4: Conditional Probability and Two Way Tables Let's review the rules of Probability Probability Rules for any Probabilistic Model: Sum of all P(Events) = 1 All probabilities must be 0 ≤ P(Events) ≤ 1 P(Event) + P(Event’s Compliment) = 1 P(certainty) = 1 and P(impossibility) = 0

Example 1: A travel agent recorded the bookings made on one Saturday. Lesson 4: Conditional Probability and Two Way Tables A two-way frequency table is a useful way to organize data that can be categorized by two variables. Example 1: A travel agent recorded the bookings made on one Saturday. France Spain Germany TOTAL Car/Ferry 15 8 28 Plane 18 14 40 u Complete the table above. Consider one of the bookings is chosen. Calculate the probability of choosing a booking for Germany. Let's say a plane booking is chosen. Calculate the probability of it being to France.

Example 2: An electrical store records the following information. Lesson 4: Conditional Probability and Two Way Tables Example 2: An electrical store records the following information. Under 21 21- 45 Over 45 TOTAL Satellite 48 19 90 Terrestrial 28 60 Cable 86 97 116 300 Complete the table above. Consider someone over 45 is chosen. Calculate the probability of them not having cable. Consider one of the records is chosen. Calculate the probability of choosing someone under 21 with cable.

P(A I B) = ---------------------­ P(B) Lesson 4: Conditional Probability and Two Way Tables Conditional Probability: Finding the probability of an event given that something else has already happened (or is true). P(A I B) is read what is the probability of A given that B has occurred. It is governed by the following formula: P( A and B) P(A I B) = ---------------------­ P(B) obviously P(B) ≠ 0 (since it has occurred) Example 3: What is the P(A|B), if P(A) = 0.6, P(B) = 0.3, P(A and B) = 0.2?

Lesson 4: Conditional Probability and Two Way Tables In the examples below, we will use the table below listing employees' years of service: Years 0-4 5-9 10-14 14+ Totals Males 12 6 17 21 56 Females 8 9 13 14 44 20 15 30 35 100 What is the probability of randomly selecting a female employee? Given that the employee is male, what is the probability that they have less than 4 years of experience? Given that the employee has between 10 and 14 years of experience, what is the probability that the employee is female? Given that the employee has more than 14 years of experience, what is the probability that the employee is male? What is the probability of randomly selected an employee with less than 14 years of experience given that they are female?