Download AP Stats Summer Assignment Probability Rules

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.