Second Semester
­Grades
­AP Test and Reviews
­Expectations(electronics, bathroom, etc)
Problem of the Day
A certain bowler can bowl a strike 70% of the time. Find the following probabilities....
the probability that she goes 3 frames without a strike.
the probability that she throws at least 1 non­strike in the next 5 frames.
`
Problem of the Day
In an AP Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty­six percent of students eat breakfast and also floss their teeth.
What is the probability that a student from this class eats breakfast but does not floss their
teeth?
A) 9% B) 11% C) 34% D) 57% E) 91%
What is the probability that a student from this class eats breakfast or flosses their teeth?
A) 9% B) 11% C) 34% D) 57% E) 91%
Is a bigger sample size always better?
Is a control group a baseline measurement?
Problem of the Day
According to the National Telecommunication and Information Administration, 56.5% of
U.S. households owned a computer in 2001. What is the probability that of three randomly
selected U.S. households at least one owned a computer in 2001?
A) 18.0% B) 43.5% C) 56.5%D) 82.0% E) 91.8%
Problem of the Day
Five juniors and four seniors have applied for two open student council positions. School
administrators have decided to pick the two new members randomly. What is the probability
they are both juniors or both seniors?
A) 0.395 B) 0.444 C) 0.506 D) 0.569 E) 0.722
Problem of the Day
A fair coin has come up “heads” 10 times in a row. The probability that the coin will come
up heads on the next flip is
A) less than 50%, since “tails” is due to come up.
B) 50%.
C) greater than 50%, since it appears that we are in a streak of “heads.”
D) It cannot be determined.
Problem of the Day
During a bank robbery, a bag of unmarked bills was thrown on the street and spilled. If you, discretely, walked by and picked up a bill without looking, is the probability that it is a $100 bill 1/7(the bill denominations are $1,$2,$5,$10,$20,$50,$100)? Why or why not?
Seniors
Non­
Seniors
Male
Dice Stuff
1 Die
­6 possible outcomes
­each equally likely
2 Dice
­36 possible outcomes
­Possible sums are 2 to 12(not equally likely)
­"Normally Distributed"
Card Stuff
52 cards in a standard deck
­13 possible cards are 2­10, Ace, King, Queen, Jack(equally likely, 4 of each)
­4 Suits are Clubs, Spades, Diamonds, Hearts
(equally like, 13 cards in each suit)
­2 colors are black:Clubs and Spades
red:Diamonds and Hearts
(how many of each color??)
­Face cards have a face on them(so......)
Chapter 15 Probability Rules!
General Addition Rule(regardless of disjoint events)
P(A U B) =
Die Roll
P(rolling a 2 or 3) = P(rolling a 2 or an even) = Multiplication Rule(Independent events)
P(A B) = P(A) P(B)
Drawing 2 cards(replace after first card) from a standard 52 card deck
P(2 kings)
P(2 non­evens)
P(2 face cards given the first card is a King) Create a Venn diagram for the following situation.
A survey of college students found that 56% live in campus residence halls, 62% have a campus meal plan, and 42% have both.
campus and doesn't have a meal plan?
What is the probability that a student lives or eats on campus?
What is the probability that a student lives in a residence hall but doesn't have a meal program?
Deriving the General Multiplication Rule
In Favor of Death Oppose Death Penalty
Penalty
Republican
.26
.04
Democrat
.12
.24
Other
.24
.10
1. What's the probability that a randomly selected voter opposes the death penalty? 2. What is the probability that a randomly selected voter is in favor of the death penalty given they are a Democrat? 3. Are party affiliation and stance on the death penalty independent? 4. Construct a Venn diagram for the situation.
Table on pg 362
Create a Venn diagram for the following situation.
A police report stated that 78% of drivers stopped on suspicion of DUI are given a breath test, 36% a blood test, and 22% both.
More with independence....
Are blood tests and breath tests for DWI suspects mutually exclusive?
Are the tests independent?
What about P(B A)?
Checking for Independence
Events A and B are independent if .......
Is the probability of having good grades as a goal independent of a student's gender?
Goals
Grades Popularity Sports Total
Boy 117
Girl 130
Total 247
50
91
141
60
30
90
227
251
478
What is the probability of having good grades as a goal, given the respondent is a girl?
Are having good grades as a goal independent of gender?
(P(good grades|girl)=P(good grades)?????)
What about the probability of having sports as a goal?
What about probability of having popularity as a goal?
Is independence = disjoint????????
4 on AP
Test
5 on AP test
Telephone surveys are typically completed in about 10% of random phone calls seeking survey results. Reasons vary, but no answer, refusal to cooperate or failure to complete were the most common. Which of the following events are independent, disjoint, or neither?
1. A=your number is randomly selected
B=you do not answer at dinnertime 2.A=as a selected subject, you complete the survey
B=as a selected subject, you refuse to cooperate
3.A=you do not answer at 11am when they call
B=you are employed full time
Drawing without Replacement
Probability of drawing 2 kings from a standard deck
Tree diagrams
Flipping a coin then rolling 1 die
A recent survey of local college students found the 44% of students are considered binge drinkers while 37% are considered moderate drinkers. Of the binge drinkers, 17% have had an alcohol related accident compared to 9% of moderate drinkers.
Consider the survey results of alcohol drinking habits and incidence of accidents.
What is the probability of an alcohol related accident?
What about the probability that a person is a binge drinker given they had an alcohol related accident?
Is the amount of alcohol you drink independent of the likelihood of an accident?
A highway safety study found that 77% of drivers in an accident were wearing a seat belt. Accident reports state that 92% of those drivers escaped serious injury. However, only 63% of non­belted drivers escaped serious injury. Construct a tree diagram with all conditional probabilities. Then find the probability that a driver who was seriously injured wasn't wearing a seat belt. Are wearing a seat belt and your level of injury independent? A manufacturing firm orders computer chips from three different companies: 10% from Company A; 20% from Company B; and 70% from Company C. Some of the computer chips that are ordered are defective: 4% of chips from Company A are defective; 2% of chips from Company B are defective; and 0.5% of chips from Company C are defective. A worker at the manufacturing firm discovers that a randomly selected computer chip is defective. What is the probability that the computer chip came from Company B?
What is the probability that a randomly selected student is female?
What is the probability that a randomly selected student ate breakfast?
What is the probability that a randomly selected student is a female who ate breakfast?
What is the probability that a randomly selected student is female, given that the student ate breakfast?
What is the probability that a randomly selected student ate breakfast, given that the student is female?
Does it appear that whether or not a student ate breakfast is independent of the student’s sex? Explain.
A local animal shelter has 24 dogs and 18 cats. 8 dogs and 6 cats are male. Find the following probabilies…..
P(Male | Cat)
P(Cat | Male)
P(Female | Dog)
Assume that 70% of teenagers who go to take the written drivers license test have studied for the test. Of those who study for the test, 95% pass; of those who do not study for the test, 60% pass. What is the probability that a teenager who passes the written drivers license test did not study for the test?
Chapter 15
Readings and Examples:pgs 342­360
Homework: pgs 361­364:5­7,9,11, 13­15, 19, 20, 27,31,33, 37, 39
Chapter 16 Readings and examples pgs 366­382