1. Today in Precalculus Go over homework Notes: More Probability Homework

2. Venn Diagrams Can be a useful way to visualize the relationships among events of a sample space. Ex: At HHS 54% of the students are girls and 43% of the students play sports. A third of the girls at HHS play sports. Rectangle: sample space (all students) Circles: events (girls and sports) students girls sports

3. Venn Diagrams Ex: At HHS 54% of the students are girls and 43% of the students play sports. A third of the girls at HHS play sports. ⅓(.54) =.18.54 -.18 =.36.43 -.18 =.25 1 -.18 -.36 -.25 =.21 What is the percent of the students who play sports are boys? If a student is chosen at random, what is the probability it is a boy who doesn’t play sports?.18.25.36.21

4. Conditional Probability & Tree Diagrams Two identical cookie jars are on a counter. Jar A contains 5 chocolate chip and 3 peanut butter cookies, while jar B contains 2 chocolate chip and 3 peanut butter cookies. Selecting a cookie at random, what is the probability that it is a chocolate chip cookie? Hint: the answer is not 7/13

5. A B.5.625.375.6.3125.1875.3 So the probability of getting a chocolate chip cookie is.3125 +.2 =.5125 because the cookie probability is dependent on the jar outcome..4.2

6. Conditional Probability Notation: P(A|B) probability of A given B P(chocolate chip|jar A)=.625 P(chocolate chip|jar B)=.4 P(A|B)= P(jar A|chocolate chip) =

7. Binomial Distribution Let p be the probability of event A and q be the probability of event A not occurring given n trials. Then the probability A occurs r times is n C n-r p r q n-r Ex: We roll a fair die four times. What is the probability that we roll: a) All 3’s

8. Binomial Distribution b) no 3’s c) Exactly two 3’s

9. Homework Pg 728: 27-31 odd, 43-49 odd