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Today in Precalculus

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

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Today in Precalculus

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  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) sports girls students

  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 .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. .3125 .625 .1875 A .5 .375 .2 .4 .5 .6 .3 B So the probability of getting a chocolate chip cookie is .3125 + .2 = .5125 because the cookie probability is dependent on the jar outcome.

  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 nCn-rprqn-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: odds 27-29, 33-37,43-49

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