General Rules
Two Way Tables & Tree Diagrams
Multiplication of Probabilities
Binomial
Geometric & Normal
100
Suppose P(A) = .35, P(B) = .6 and P(A nB) = .27.
Determine P(Ac)
What is...
1-.35=.65
100
A researcher interested in eye color versus success in a math program collected the following data from a random sample of 2000 high school students.
What is the probability that a student from this group fails the math program?
What is...
P(fail)=200/2000=.10
100
The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot),
What type of event is this describing?
What is...
Binomial
100
The AP Statistics exam includes 40 multiple choice questions, each with 5 answer choices. Suppose you believe you have forgotten everything and must guess (randomly choose one of the five answers choices) on every question. Let x represent the number of correct responses on the test.
Prove the type of distribution that X has.
What is ...
BINS
B-right/wrong, I- each question independent N-n=40, S=p=.20
100
The Stat Master computer game allows players to replenish their brain power (check their notes) only 10% of the time after successfully completing a level. Consider the random variable x, where x = number of levels that must be successfully completed until brain power is replenished.
Prove what type of distribution this would be.
What is ...
Geometric
BIUS
B-success/not, I-each level independent, U-play until brain power replenished, S-p=.10
200
Suppose P(A) = .35, P(B) = .6 and P(A nB) = .27.
Find P(A U B)
What is...
.35+.6-.27=.68
200
A researcher interested in eye color versus success in a math program collected the following data from a random sample of 2000 high school students.
What is the probability that a student from this group fails that math program given that he/she has blue eyes?
What is ...
P(fail|blue)=10/100=.10
200
The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot).
What is the probability that Michael misses all three shots?
What is....
(.1)(.1)(.1)=.001
200
The AP Statistics exam includes 40 multiple choice questions, each with 5 answer choices. Suppose you believe you have forgotten everything and must guess (randomly choose one of the five answers choices) on every question. Let x represent the number of correct responses on the test.
What is your expected score on the exam?
What is...
E(x)=np=40(.20)=8
200
The Stat Master computer game allows players to replenish their brain power (check their notes) only 10% of the time after successfully completing a level. Consider the random variable x, where x = number of levels that must be successfully completed until brain power is replenished.
What is the probability that at most 2 levels must be successfully completed?
What is ...
geomcdf(.10,1,2)=.19
300
Suppose P(A) = .35, P(B) = .6 and P(A nB) = .27.
Find P(A|B)
What is ...
.27/.6=.45
300
A researcher interested in eye color versus success in a math program collected the following data from a random sample of 2000 high school students.
Are blue eyes and failing math independent?
What is...
P(A|B)=P(A)
=.10=.10 so they are independent
300
The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot)
What is the probability that Michael makes at least one of the three shots?
What is...
P(a least 1)=1-P(none)
1-.103=.999
300
The AP Statistics exam includes 40 multiple choice questions, each with 5 answer choices. Suppose you believe you have forgotten everything and must guess (randomly choose one of the five answers choices) on every question. Let x represent the number of correct responses on the test.
Compute the standard deviation of x?
What is...
sqrt(np(1-p)
=sqrt(40(.20)(.80))
=2.53
300
The Stat Master computer game allows players to replenish their brain power (check their notes) only 10% of the time after successfully completing a level. Consider the random variable x, where x = number of levels that must be successfully completed until brain power is replenished.
What is the probability that exactly five levels must be successfully completed?
What is....
p(x=5)=geompdf(.1,5)=.06561
400
Suppose P(A) = .35, P(B) = .6 and P(A U B) = .27.
Are A and B independent events?
What is...
P(A)=P(A|B)
=.35 does not equal .45 so they are not independent
400
Of the 60 obese teenagers in a recent study, 15 had type II diabetes, 20 had high blood pressure, and 10 had both high blood pressure and type II diabetes. Suppose one of these 60 obese teenagers is randomly selected.
If the obese teenager does NOT have high blood pressure, what is the probability that he or she also does not have type II diabetes?
What is ...
P(Dc|Bc)=35/40=.875
400
The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot)
What is the probability that Michael makes the first shot but not the second or third?
What is...
(.90)(.10)(.10)=.009
400
The AP Statistics exam includes 40 multiple choice questions, each with 5 answer choices. Suppose you believe you have forgotten everything and must guess (randomly choose one of the five answers choices) on every question. Let x represent the number of correct responses on the test.
What is the probability that you will get exactly 25 questions correct?
What is ...
P(x=25)=binompdf(40,.20,25)=0
(.00000000475)
400
The Stat Master computer game allows players to replenish their brain power (check their notes) only 10% of the time after successfully completing a level. Consider the random variable x, where x = number of levels that must be successfully completed until brain power is replenished.
What is the probability that more than three levels must be successfully completed?
What is ...
1-geomcdf(.1,1,3)=.729
500
Suppose the probability that a construction company will be awarded a certain contract is
.25, the probability that it will be awarded second contract is .21, and the probability that it will get both contracts is .13. What is the probability that the company will win at least one of the two contracts?
P( 1 or 2)= P(1)+P(2)-P(1 and 2)
.25+.21-.13=.33
500
Two office assistants at Penny Lane High School are responsible for getting the daily tardy list to the appropriate principals by 3:00pm daily. Rudy works on the lists 30% of the days and Fawn works on the tardy lists 70% of the days. Rudy fails to get the lists to the correct principals in time 10% of the time (which would make him tardy with the tardy lists). Fawn, not much better, manages to get the tardy lists to the correct principals 92% of the time. Let’s say you are Principal Sac and the tardy list is late. What is the probability that today Rudy is responsible for the list?
What is ...
P(Rudy|Late)=.03/.086=.349
500
The probability that Michael misses a free throw shot is .1. If he goes to the line to shoot three free throws (due to a foul on a three-point shot)
What is the probability that Michael makes all 3 shots?
What is...
(.9)(.9)(.9)=.729
500
The AP Statistics exam includes 40 multiple choice questions, each with 5 answer choices. Suppose you believe you have forgotten everything and must guess (randomly choose one of the five answers choices) on every question. Let x represent the number of correct responses on the test.
Overall, you believe you can do really well on the free response section. You did not study for the multiple choice section because you figured out that you would probably only need 16 questions correct to earn college credit in the course. What is the probability that you correctly answer at least 16 problems?
What is ....
binomcdf(40,.20,16,40)=.002936
500
A machine that puts the center holes in blank CDs operates in such a way that the distribution of the diameter of the holes may be approximated by a normal distribution with a mean of 1.5 cm and a standard deviation of .1 cm. The specifications require the diameters of the holes to be between
1.4 and 1.6 cm. A CD not meeting the specifications is considered defective. (A center hole too small would not fit properly in a CD burner; a hole too large may cause the CD to slide during burning and ruin the quality of the music.) What proportion of CDs produced by this machine are defective due to an improperly sized center hole?
What is ....
normcdf(-oo,-1,0,1)=.159x2=.317