Compound OR Probability

Transcription

1 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 inclusive, 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

2 Using a Two-Way Table To Compute Compound Event Probability Computing P(A or B) 0. If not already done, total the table. 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)

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4 Math Tech IIII, Apr 18 Probability Using a Two-Way Table to Compute Probability Conditional Probability Book Sections: 3.3 Essential Questions: How can I compute the probability of any event? What is a condition and conditional probability? How can I use a table to compute conditional probability? Standards: PS.SPCR.3,.4,.5,.6

5 What is a Condition? A condition is a limitation on the data set to a specific sub-set (of the data). In the context of a two-way table, a condition specifies a row or a column of the table.

6 How does a Condition Show Itself? A condition is indicated by the word given. Given starts a condition that limits a data set. Example: Given that today is Tuesday, there is no point in considering any other day.

7 Using the Two-Way Table A two-way table becomes a limited setting based on the condition. Restrict the table based on the condition, then compute a probability from within it. This means working within the row or column based on the condition. This is a simple probability computation (form a ratio). Because of the limitation placed on the data set by the condition, we do not use the table grand-total in this computation. Use the row or column total in this case.

8 Table Example We use our prior example as our first example. The table is totaled. The health care option and dependent child status of Titan Corporation Employees are summarized in the table. HMO BC/BS None Total Dep Child No Child Total A Titan employee is randomly chosen. Compute each probability: 1) Given that the employee has the HMO, what is the probability that they have no dependent children? 2) Given that the employee has a dependent child, what is the probability that they have no coverage?

9 Using a Two-Way Table To Compute Conditional Probability Computing Given A, compute P(B) step-by-step 0. If not done, 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, circle that row or column. 2. Find event B on row or column heading, extract that value from the column or row identified by A This is the numerator of the probability ratio. 3. The denominator of the ratio is the row or column total of A. Simplify the ratio, or show as a decimal.

10 Examples The following table shows the science taken by 80 seniors and their gender at Bayside High School, Los Angeles, Ca: Gender/Science Biology Chemistry Physics Total Female Male Total Compute each probability: One student is randomly chosen: 1) Given that the student takes biology, compute P(male) 2) Given that the student is female, compute P(physics) 3) Given that the student takes chemistry, compute P(female)

11 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 (Previous now done) 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 (Today) If compound event probability, P(a or b) (Before spring break) No matter what, total the table if it is not already done!

12 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: or

13 Example A study was conducted to determine whether there is a relationship between jogging and blood pressure. A random sample of 210 subjects was selected. The following results were obtained: Low BP Moderate BP High BP Joggers Non-joggers

14 Example If a random participant were selected, compute each probability: Low BP Moderate BP High BP Joggers Non-joggers a) Given moderate bp, P(jogger) b) P(low bp or jogger)

15 Things I Would Know These two events are mutually exclusive. Being in Virginia and being in Georgia. In a probability computation, what does a condition do? It limits the choices within a data set. Why does inclusive compound event probability involve a subtraction of P(A and B)? A and B have some overlap, and the value of that overlap has been counted twice.

16 Homework: None Class work: CW 4/18/17, 1-4