Math Tech IIII, Apr 14

Transcription

1 Math Tech IIII, Apr 14 Probability Using a Two-Way Table to Compute Probability - Compound Event Probability Book Sections: 3.3 Essential Questions: How can I compute the probability of any event? How can I use a table to compute compound event probability and experimental probability? Standards: PS.SPCR.3,.4,.5,.6

2 Probability Probability is, was, and always will be a number between 0 and 1 (inclusive).

3 Example A bag has 5 marbles in it. One is red, 2 are pink, and 2 are blue. One marble is selected. Compute: P(pink or red)

4 Using the Two-Way Table The very first thing to always check for in a 2-way table is that it is totaled (rows and column added) and that you have a grand total for the table. If it is not done, make that your FIRST STEP in this process.

5 Mutually Exclusive Events Events A and B are mutually exclusive if they cannot occur at the same time. Events A and B are inclusive if there is some (common) outcome that can be both events.

6 Mutually Exclusive Events Events A and B are mutually exclusive if they cannot occur at the same time. Sample Space A B Not occurring simultaneously means there is no overlap between the events

7 Not Mutually Exclusive The opposite of mutually exclusive is inclusive which means events can occur at the same time. We can say inclusive or not mutually exclusive to describe this phenomenon.

8 Inclusive Events Events A and B are not mutually exclusive if they can occur at the same time. Sample Space A B A B The overlap (green section) is A B, also known as A and B

9 Compound OR Probability If two events, A and B are mutually exclusive, then P(A or B) = P(A) + P(B) If two events, A and B are not mutually exclusive, then P(A or B) = P(A) + (B) P(A and B) Where (A and B) are outcomes of both A and B at the same time

10 The Two-Way Table A two-way table is a display of connected data, which is displayed in rows and columns The connections of rows and columns define data relationships Row to row or column to column relationships are mutually exclusive Row to column relationships are inclusive Row and column intersections display the value of set intersections

11 Table Example Compute the following probabilities if 1 person is randomly selected: P(HMO or have dep children) P(HMO or have no coverage) HMO BC/BS None Total Dep Child No Child Total

12 Using a Two-Way Table To Compute Compound Event Probability Computing P(A or B) 0. If not a given, sum every row and column (including your new totals row and column) to compute every event total and a grand total 1. Find event A on row or column heading, scribe a line 2. Find event B on row or column heading, scribe a line 3. If lines are parallel add row or column totals, put answer over grand total, simplify (ME probability) 4. If lines cross, add row and column totals, subtract cross value put answer over grand total, simplify (I probability)

13 Read the Problem Decide Upon reading any problem that contains the word or, you must Decide if the two events are mutually exclusive or inclusive If inclusive, figure the points of overlap and find that probability Apply the correct addition rule form that applies to the problem The table lines will guide you in these decisions

14 Examples On the first day of season practice, a high school s football players hair and eye color were noted. The results are summarized below. Compute each probability if 1 player is selected: P(red hair or green eyes) P(blue eyes or green eyes) P(black or brown hair) P(blond hair or hazel eyes)

15 Three Ways of Using a Table How do you know what is being asked Read the problem If a simple probability statement P(event) find the event total cell and divide that entry by grand total (Done with this one) If compound event probability, P(a or b), draw lines, determine case add and subtract (if applicable), divide by grand total If conditional probability, you can tell by the word given Given a, find P(b) work within row or column of a, find b, divide by row or column total No matter what, total the table if not already done so

16 Example A student is randomly chosen: Compute: P(plays a sport or takes a foreign language) P(does not play a sport or does not take a language)

17 How Will I Know Which is Which? The problem statement tells you. Simple probability P(event), example P(red), Tip: 1 thing Conditional probability, Given A, P(B), example Given red, P(blue), Tip: the word given Compound event P(A or B), example P(red or blue), Tip: the word or

18 Homework: None Class work: CW 4/14/16, 1-4