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AP Stats Summer Assignment Probability Rules To complete this assignment, you need to view videos from YouTube. The videos are about 10 minutes and 4 minutes. After viewing, answer the problems below on a separate sheet of paper. I. Title: DuPage Statistics: Basic Rules of Probability http://www.youtube.com/watch?v=3HCu_7O1oEY Main Concept that you need to be comfortable with o Complimentary Events o Probability notation (“set” notation) o Addition Rule (aka “or” rule, i.e. A B ) o Mutually Exclusive Events (aka “disjoint”, although not mentioned in video) o Multiplication Rule (aka “and” rule, i.e. A B ) o Sample Space Illustrating Problems using Diagrams o Venn Diagrams can be used to visualize problems. They can show how an attribute or characteristic is shared between 2 outcomes (the intersection is the shared attribute). They can also be used when outcomes are mutually exclusive or disjoint (in this case the circles do not intersect). At the 5:30 mark, there is an example of finding the probability of choosing a diamond or a queen from a standard deck of cards. The Venn Diagram would look like this: Diamond Queen 13/52 4/52 Overlap of a Diamond and Queen 1/52 o II. Create your own Venn Diagram for the example of P( H 6) at the 7:00 mark. Tree Diagrams are useful visual tools too. They can be used equally well for independent events as well as dependent Create a tree diagram for the example at the 5:30 mark (the Diamond OR queen example above (with replacement = independent events) Create a tree diagram for the example at the 9:00 mark for drawing 2 diamond cards (without replacement = dependent events) Title: Multiplication Rule (Probability “and”) http://www.youtube.com/watch?v=Q_7PR9kRXWs&feature=related Additional explanation of the multiplication rule Answers the problem below/on back Probability Problems: 1. For each of the following, list he sample space and tell whether you think the outcomes are equally likely. Reminder-the sample space lists all possible outcomes for the variable of interest. a. Roll two dice, record the sum of the numbers b. A family has 3 children; record the genders in order of birth c. Toss four coins; record the number of tails d. Toss a coin 10 times; record the longest run of heads. 2. Each student in a class of 30 studies one foreign language and one science. The students’ choices are shown in the table below. Chemistry (C) Physics (P) Biology (B) Totals French (F) 7 4 3 14 Spanish (S) 1 6 9 16 Totals 8 10 12 30 a. Find the probability that a randomly chosen student studies chemistry. b. Find the probability that a randomly chosen student studies chemistry given that the student studies French. c. Are the events “student studies chemistry” and “student studies French” independent? 3. A card is randomly drawn from a standard deck. a. Show that the events “jack” and “spade” are independent. b. Create a diagram you could use to find the probability of drawing the jack of spades. c. Show that the rule P( A B) P( A) P( B) can be used to find the probability of drawing the jack of spades. 4. A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. What is the probability that a car chosen at random will need a. No repairs? b. No more than one repair? c. Some repairs? 5. Real estate ads suggest that 64% of homes for sale have garages, 21% have swimming pools, and 17% have both features. a. Create a visual representation of this situation. b. What is the probability that a home for sale has i. A pool or a garage? ii. Neither a pool nor a garage? iii. A pool but no garage? c. Rewrite the problems from part b) in probability notation. For example, the probability of having a pool and a garage would be written as P( P G) where P represents a pool and G represents a garage. 6. Seventy percent of kids who visit a doctor have a fever, and 30% of kids with a fever have sore throats. What’s the probability that a kid who goes to the doctor has a fever and a sore throat? Create a visual diagram to represent this situation, write the problem in probability notation, and find the requested probability.