VISUALIZING PROBABILITIES AND TABLE FREQUENCY.pptx

Tables, histograms, bar graphs and pie charts are the most common visual representations of probability distributions.

1. Can you guess the picture?

2. Can you guess the picture?

3. Can you guess the picture?

4. Can you guess the picture?

5. Can you guess the picture?

6. Visualizing Probabilites

7. Learning Objectives define what is contingency table and Venn diagram; illustrates problems using contingency table and Venn diagram; and solve problems involving conditional probability; show perseverance and determination in visualizing probabilities.

8. Contingency Table Venn Diagram Lesson Outline

9. Contingency Table A contingency table provides a way of portraying data that can facilitate calculating probabilities. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another.

10. Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data: a. Find P (Driver is a cell phone user). b. Find P (driver had no violation in the last year). c. Find P (Driver had no violation in the last year AND was a cell phone user). d. Find P (Driver is a cell phone user OR driver had no violation in the last year). e. Find P (Driver is a cell phone user GIVEN driver had a violation in the last year). (The sample space is reduced to the number of drivers who had a violation.) f. Find P (Driver had no violation last year GIVEN driver was not a cell phone user). (The sample space is reduced to the number of drivers who were not cell phone users.

11. a. (number of cellphone users)/(total number in study)= 305/755 or 61/151 b.(number that had no violation)/(total number in study)= 685/755 or 137/151 c. 280/755 or 56/151 d.(685/755+305/755-280/755)= 710/755 or 142/151 e. 25/70 or 5/14 f. 405/450 or 9/10

12. Venn Diagram A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space (S) together with circles or ovals. The circles or ovals represent events. It can often help us visualize relationships between events and compound events. We can visualize the entire rectangle as the Sample Space and areas in the circles as corresponding to probabilities.

13. In a class of 50 students, 30 take Philosophy, 23 take Sociology, and 12 take both. What is the probability that a randomly selected student? a) Takes Sociology b) Takes both Philosophy and Sociology c) Does not take Philosophy d) Takes Sociology but not Philosophy e) Takes Philosophy given Sociology f) Takes Philosophy or Sociology g) Takes neither Philosophy nor Sociology h) Takes Sociology or Philosophy but not both.

14. a) 23/50 b) 12/50 or 6/25 c) 20/50 or 2/5 d) 11/50 e) 12/23 f) 41/50 g) 9/50 h) 29/50

15. Activity No. 23 A survey of licensed drivers asked whether they had received a speeding ticket in the last year and whether their car is red. The results of the survey are shown in the contingency table to the right. Find the probability that a randomly selected survey participant: a. has a red car. b. has had a speeding ticket in the last year. c. has a red car and has not had a speeding ticket in the last year. d. has a red car or has had a speeding ticket in the last year. e. has had a speeding ticket in the last year given they have a red car. f. who has received a speeding ticket in the last year also has a red car. I. Solve the probability of the following using the contingency table.

16. II. Illustrates the problem using Venn diagram and solve the probability of the following. Among the 95 books on a bookshelf, 72 are fiction, 35 are hardcover, and 28 are both fiction and hardcover. a) Create a Venn diagram for the information. b) What is the probability that a book is fiction and paperback? c) What is the probability that a book is fiction given it is hardcover?

17. A recent survey asked SINHS’ians students if they regularly eat breakfast and if they regularly floss their teeth. Use the completed Venn Diagram to fill in the corresponding contingency table. 12 8 Breakfast Floss Breakfast No Breakfast Total Floss No Floss Total

18. 100 people were asked if they play basketball or badminton. 36 said they play basketball 56 said they play badminton 20 said they play both. Illustrates this information on a Venn Diagram and contingency table. Find the probability that a randomly selected survey participant: Play basketball or badminton Play basketball and badminton Play badminton given that they play basketball Neither basketball nor badminton