Sample Space, Events, & Probability Models
Probability Calculations
Conditional Probability
Venn Diagrams (& 1 two-way table)
Older Problems (ch.1 to ch.4)
100
You flip two fair coins at once and record the face they land on. What is the sample space for this experiment?
{HH,HT,TH,TT}
100
In a bag, there are 8 red marbles and 4 green marbles. What is the probability of drawing either a red marble or a green marble on a single draw?
1.0
100
A deck of cards contains 52 cards. What is the probability of drawing a red card (heart or diamond) given that you have already drawn a face card (king, queen, or jack)?
0.5
100
In a class of 30 students, 15 like math, 20 like science, and 10 students like both subjects. Create a Venn diagram and write the appropriate proportion within each circle.
100
Draw to normal curves on the same axis. One with a large mean and small spread and one with a small mean and larger spread.
I'll judge the drawing.
200
A new bill has been proposed and a survey has gone out to collect the ages of those in favor of the bill. What is X?
0.26
200
In a standard deck of cards, what is the probability of drawing either a red card or a face card (king, queen, or jack)?
32/52
200
In a bag, there are 8 red marbles and 4 green marbles. If you randomly select one marble and don't replace it, what is the probability that the second marble you select is red, given that the first one was also red?
7/11
200
Researchers surveyed 100 students on which superpowers they would most like to have. The two-way table below displays data for the sample of students who responded to the survey. What is the probability that a student chose fly as their superpower ability given they are male? What about P(male|fly)=?
P(fly|male)=.5416
P(male|fly)=.6842
200
You are given the test scores of 5 students. What is the mean and standard deviation?
{79.2, 68.9, 88.0, 98.3, 83.2}
mean = 83.52; stdv = 10.852
300
A box contains 4 red balls, 1 green ball, and 2 blue ball. If you draw two balls without replacement, what is the sample space for this experiment?
{RR,RG,RB,GR,GB,BR,BG,BB}
300
Choose an American household at random and record the number of vehicles they own. Here is the probability model if we ignore the few households that own more than 5 cars:
A housing company builds homes with two-car garages. What percentage of households have more cars than the garage can hold?
0.20
300
A box contains 3 white balls and 2 black balls. You draw two balls without replacement. Come up with a probability model for this. That is, come up with the sample space and the probabilities for each outcome.
{WW,WB,BW,BB}(corresponding probabilities)-->{6/20,6/20,6/20,2/20}
300
In a group of 50 people, 30 have a pet (dogs or cats), 20 people have dogs, and 15 have cats. How many people have both dogs and cats, and how many have neither?
5 people have both, and 20 have neither.
300
A statistician wants to test a pharmaceutical company's new medicine. However there have been preliminary results indicating less effectiveness if the patient has previously had COVID. What type of experiment should the statistician use?
Randomized block design.
400
What is the probability that a person's favorite music genre is rap or rock? What is the probability that a person's favorite music genre is rock and pop?
391/1000; 0/1000
400
You are rolling an 8-sided die. What is the probability of getting either a 3 or an odd number on a single roll?
.50
400
In a city, 60% of the residents own a car, 40% own a bike, and 20% own both a car and a bike. If you randomly select a resident, what is the probability that they own a car given that they own a bike?
0.50
400
In a town, 60% of the residents like baseball, 45% like soccer, and 30% like both sports. What percentage of residents do not like either baseball or soccer?
0.25
400
What is the slope of the LSRL if ybar = 103, xbar = 12, sy=10, sx = 2.4, and r =-.5.
b=-2.083
500
A probability model has to follow two main rules. Come up with a probability model for a 6-sided die (does not have to be fair) that violates 1 rule but not the other rule.
Example {1,2,3,4,5,6}(corresponding probabilities)-->{5/6,-2/6,3/6,0,0,0}
500
In a bag, there are 12 marbles: 6 are red, 3 are green, and 3 are blue. You draw 3 marbles one by one without replacement. What is the probability that you draw all red marbles?
1/11
500
100 people are asked if they like coffee or tea. The Venn diagram below represents their answers. Find P(coffee); P(tea); P(coffee|tea); P((coffee or tea)C)
P(coffee) = .60,
P(tea) = 0.40,
P(coffee|tea) = 0.625, and
P((coffee or tea)C)=0.25
500
The entire boys basketball team at a small school is comprised of 8 students. You match all 8 students into pairs based on similar athletic ability. You then flip a coin to randomly select a total of 4 boys and survey them on school athletics. This can best be described as...?
Stratified Random Sampling