1. Adding Probabilites 0.5

2. Probability: the likelihood the event will occur. must be a # between 0 and 1 Certain to occur: probability of 1 Cannot occur: probability of 0 Equally likely to occur or not occur: probability of ½ (50% or.5)

3. (Theoretical) Probability When all outcomes are equally likely that an event will occur is: P(A) = number of outcomes in A total number of outcomes Simply called the probability of an event

4. Example 1: Find the probability. A spinner has 8 equal-size sectors numbered from 1 to 8. a) Spinning a 6 b) Spinning an even number c) Spinning a number greater than 5

5. Experimental Probability used when it is impossible or inconvenient to find the theoretical probability. used by performing an experiment, conducting a survey, or looking at the history of the event.

6. Example 2: Find the probability. Ninth graders must enroll in one math class. The enrollments of ninth grade students during the previous year are shown in the bar graph. Find prob. that a randomly chosen student from this year’s 9 th grade class is in enrolled in a) Consumer Math b) Algebra 1 or Intro to Algebra

7. Compound Events Union: when you consider ALL the outcomes for either of two events A and B. (A, B, A&B) Intersection: when you consider only the outcomes shared by both A and B. (A&B) Mutually Exclusive Events: if there is no intersection of A & B (Nothing in common)

8. IF A & B INTERSECT: P(A or B) = P(A) + P(B) – P(A&B) (Since P(A) and P(B) both include P(A & B)) IF A & B ARE MUTUALLY EXCLUSIVE:P(A or B) = P(A) + P(B)          BA          BA          BA UNION of A and BINTERSECTION of A and BINTERSECTION is empty P(A or B)P(A and B)mutually exclusive events

9. Example 3 One six-sided die is rolled. a) What is the probability of rolling a multiple of 3 or a 5? b) What is the probability of rolling a multiple of 3 or a multiple of 2?

10. Example 4 In a poll of high school juniors, 6 out of 15 took a French class and 11 out of 15 took a math class. Fourteen out of 15 took French or math. What is the probability that a student took both French and Math?

11. Example 5 You have an equally likely chance of rolling any value on each of two dice. Find the probability of rolling…. a) a sum of either 3 or 11 b) doubles or a sum or 8 c) a nine on exactly one die

12. Warm up In a survey of 200 pet owners, 103 owned dogs, 88 owned cats, 25 owned birds, and 18 owned reptiles. a) None of the respondents owned both a cat and a bird. What is the probability that they owned a cat or a bird? b) Of the respondents, 119 owned a dog or a reptile. What is the probability that they owned a dog and a reptile?

13. Example 6: Find the probability. Five cards are drawn from a standard 52-card deck. a) Choosing exactly all red cards b) Choosing exactly 2 even numbered card and 3 face cards c) Choosing exactly three fives Probability involves Combinations!!

14. Example 7 Seven marbles are chosen at random from a jar containing 15 green marbles and 11 white marbles. Find the probability of the following: A) choosing 4 green marbles and 3 white marbles B) choosing exactly one white marble