1.  Jack rolls a 6 sided die 15 times and gets the following results: 4, 6, 1, 3, 6, 6, 2, 5, 6, 5, 4, 1, 6, 3, 2. Based on these results, is Jack rolling a fair die? Justify your answer.

2.  Okay, only 1 more.  List the 3 (with names) that we learned yesterday ;)

4.  Suppose that among the 6000 students at a high school, 1500 are taking honors courses and 1800 prefer watching basketball to watching football. If taking honors courses and preferring basketball are independent, how many students are both taking honors courses and prefer basketball to football?

5.  Know  Vs  Prove!

6.  Rolling two dice  Drawing cards WITH replacement  Drawing marbles WITH replacement  Something with replacement ;)

7.  Drawing cards/marbles WITHOUT replacement  Age and height  Time studying and grade on test  Shoe size and shirt size

8.  General Multiplication Rule P(A and B) = P(A)P(B|A)

9. P(B|A) is read “the probability of B given A.” It asks you to find the probability of B knowing that A has occurred. Try it- What is the probability of drawing a red card from a deck if you KNOW you already drew a red card? conditional probability-

10.  You draw two cards from a deck of cards without replacement. What is the probability of drawing two spades?  P(A and B) = P(A)P(B|A) =

11.  A coach’s desk drawer contains 3 blue pens, 5 black pens, and 4 red pens. What is the probability that he selects a black pen followed by a red pen, if the first pen is not replaced? (look familiar?)

12.  The ball bin in the gym contains 8 soccer balls, 12 basketballs, and 10 kickballs. If Coach Myers selects 2 balls at random and does not replace the first, what is the probability that she selects 2 basketballs?

13.  Solve the general mult rule for P(B|A)

14.  Suppose your teacher has given 2 pop quizzes this week. Seventy percent of her class passed the first quiz and 50% passed both quizzes. If a student is selected at random, what is the probability that he or she passed the second quiz, given that the student passed the first quiz?

15.  At a shoe store yesterday, 74% of customers bought shoes, 38% bought accessories, and 55% bought both shoes and accessories. If a customer is selected at random, what is the probability that he bought accessories, given that he bought shoes?

16.  Standardized tests like to trick you (we all know that). Don’t fall for it!  If a question asks “Are the events independent” we must prove or disprove.  “How” you say…?

18.  A weatherman said there is a 30% chance of rain tomorrow and 50% chance of sun tomorrow. He also claims there is a 15% chance of sun in the morning and rain in the afternoon. Are these events independent?

19.  Lots of review. Don’t think you’re doing it wrong!