1. by Trip Lenahan by Trip Lenahan2007-2008

2. What is Probability? ► Probability is the likelihood of something happening. ► Probability is expressed as a fraction as the number of desired outcomes over the number of possible outcomes.

3. Probability ►T►T►T►The highest probability of an event occurring is: 1 ►T►T►T►The lowest probability of an event occurring is: 0

4. Professions That Use Probability ► Insurance companies ► Professional card players ► Casino operators ► Athletes ► Sports Analysts ► Statistics keepers ► Secretaries ► Accountants ► Doctors

5. Two-Step Procedure To determine probability, one may use this two-step procedure: To determine probability, one may use this two-step procedure: 1. Determine and count all logical possibilities 2. Determine and count all desired possibilities or “winners”

6. Probability Formula The Probability Formulas are as follows: p= number of winners p= number of winners total number of possibilities total number of possibilitiesOR p= winning region p= winning region total possible region total possible region

7. Example of Probability #1 ► If there are 10 balls (7 red, 3 green) then the likelihood of selecting a red ball on one attempt is …. 7 red balls (winners) 7 red balls (winners) 10 total balls (total possibilities) 10 total balls (total possibilities)

8. Example of Probability #2 Problem : If one of the four points is picked randomly, what is the probability that the point lies on CA? A B C D

9. Example of Probability #2 (cont) ► To solve this problem, we first list all possibilities ABCD ► Then, we circle the winners ABCD A B C D

10. Example of Probability #2 Solution Therefore the probability of the selected point being on the angle is: Winners = 3 Winners = 3 Possibilities 4

11. Practice Problem #1 If one of the four angles is selected randomly, what is the probability that the angle is acute? A. ¼B. ½ C. ¾D. 1

12. Example of Probability #3 Problem : If two of the four points are picked at random, what is the probability that both lie on CA? A B C D

13. Example of Probability #3 ABBCCD ACBD AD Probability= 3 = 1 6 2 A B C D

14. More Probability (pg 52 #10) If point B is chosen on AC, what is the probability that -5 < B < 7? AC -2010-57 A. 2/5B. 12/10 C. 1/15 D. 3/5....

15. Still more… (pg 52 #11) The second hand of a clock sweeps continuously around the face of the clock. What is the probability that at any random moment the second hand is between 7 and 12? The second hand of a clock sweeps continuously around the face of the clock. What is the probability that at any random moment the second hand is between 7 and 12? A. 7/12B. 7/60 C. 12/60 D. 5/12

16. Last one… (pg 52 #15) If a point is chosen at random in rectangle ABCD, what is the probability that: If a point is chosen at random in rectangle ABCD, what is the probability that: a. It is in square SQUA? A. 2/9B. 1/5 C. 3/5D. 1/3 9 2 3 5 CB AD S Q U

17. Last one (really)… (pg 52 #15) If a point is chosen at random in rectangle ABCD, what is the probability that: If a point is chosen at random in rectangle ABCD, what is the probability that: b. It is not in square SQUA? A. 2/5B. 1/5 C. 3/5D. 4/5 9 2 3 5 CB AD S Q U