Name:
Probability and Statistics – Ms. D’Amato
Date:
Block:
Chapter 11: Understanding Randomness
1.
Besides flipping a coin, another device that we can use for probability is a spinner. The spinner
I have has 4 sectors colored red, yellow, green, and blue. The probability of landing on red is
0.10, the probability of landing on yellow is 0.20, the probability of landing on green is 0.20
and the probability of landing on blue is 0.50.
Components:
Outcomes:
Assign digits:
Suppose you spin the spinner 5 times. Using a table of random digits, starting at row 40, estimate the
probability that you will land on blue all five times.
Trial Number
1
2
3
4
5
Random Digits
Result
Exactly 5 blues?
Probability of exactly 5 blues?
2.
Instead of a spinner, I now have a 5-sided die containing the numbers 1 through 5. Each
number has the same probability of 0.20.
Components:
Outcomes:
Assign digits:
Suppose you roll the die 5 times. Using a table of random digits, starting at row 11, column 6, to
estimate the probability that you will get one of each numbers.
Trial Number
1
2
3
4
5
Random Digits
Result
One of each number?
Probability of one of each number?
Chapter 14: From Randomness to Probability
3.
The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will
determine what happens next. Are the following probability assignments possible? Why or
why not?
a)
b)
c)
d)
e)
4.
Red
0.25
0.10
0.20
0
0.10
Blue
0.25
0.40
0.50
0
-1.50
If a peanut M&M is chosen at random, the chances of it being of a particular color are shown in
the following table.
Color
Probability
5.
Probabilities of…
Yellow
Green
0.25
0.25
0.20
0.30
0.30
0.40
0
1.00
0.20
1.20
Brown
Red
Yellow
Green
Orange
0.3
0.2
0.2
0.2
0.1
a)
Find the probability of randomly drawing a blue peanut M&M.
b)
Find the probability of randomly drawing a Red or a Yellow.
Blue
If P(A) = 0.24 and P(B) = 0.52 and A and B are mutually exclusive, what is P(A or B)?
6.
What does it mean when two events are disjoint (mutually exclusive)?
7.
Which of the following pairs of events are disjoint (mutually exclusive)?
8.
9.
a.
Event A: the odd numbers; Event B: the number 5
b.
Event A: the even numbers; Event B: the numbers > 10
c.
Event A: the numbers < 5; Event B: all negative numbers
d.
Event A: the numbers > 100; Event B: the numbers < -200
A box contains six red tags numbered 1-6 and four white tags numbered 1-4. One tag is drawn
at random.
a)
Calculate the probability of choosing red.
b)
Calculate the probability of choosing an even number.
The data for this experiment are provided below. These are real data, and you may construct a
similar experiment by looking for graphs and other data displays in a newspaper or magazine.
Number of Fires of Various Types
Among 100 Typical Home Fires
Cause of Fire
Number Reported
Heating system
22
Cooking
15
Electrical system
8
Smoking
7
Appliances
7
Other
41
Suppose a fire starts in a home down the street from where you live. Using the table above,
estimate the probability that:
a)
It is a cooking fire.
b)
It started in the electrical wiring.
10.
c)
It was not caused by smoking.
d)
It was caused by the heating system or appliances.
e)
It was caused by someone cooking or smoking.
A Gallup poll in March 2001 asked 1005 U.S. adults how the United States should deal with the
current energy situation: by more production, more conservation, or both? Here are the
results:
Response
More production
More conservation
Both
No opinion
Total
Number
332
563
80
30
1005
If we select a person at random from this sample of 1005 adult,
11.
a)
what is the probability that the person responded “More production”?
b)
what is the probability that the person responded “Both” or had no opinion?
Problem #9 shows the results of a Gallup Poll about energy. Suppose we select three people at
random from this sample.
a)
What is the probability that all three responded “More conservation”?
b)
What is the probability that none responded “Both”?
12.
13.
You roll a fair die three times. What is the probability that
a)
you roll all 6’s?
b)
you roll all odd numbers?
c)
none of your rolls get a number divisible by 3?
d)
you roll at least one 5?
A certain bowler can bowl a strike 70% of the time. What is the probability that she
a)
goes three consecutive frames without a strike?
b)
makes her first strike in the third frame?
c)
has at least one strike in the first three frames?
d)
bowls a perfect game (12 consecutive strikes)?
14.
15.
Suppose that in your city 37% of the voters are registered as Democrats, 29% as Republicans,
and 11% as members of other parties (Liberal, Right to Life, Green, etc.). Votes are not aligned
with any official party are termed “Independent.” You are conducting a poll by calling
registered voters at random. In your first three calls, what is the probability you talk to
a)
all Republicans?
b)
no Democrats?
c)
at least one Independent?
You bought a new set of four tires from a manufacturer who just announced a recall because
2% of those tires are defective. What is the probability that at least one of yours is defective?
Chapter 15: Probability Rules!
16.
A check of dorm rooms on a large college campus revealed that 38% had refrigerators, 52% had
TVs, and 21% had both a TV and a refrigerator.
a)
Create a Venn diagram with accurate values that represent this scenario.
b)
What’s the probability that a randomly selected dorm room has a TV but no
refrigerator?
c)
What’s the probability that a randomly selected dorm room has a TV or a refrigerator
but not both?
d)
What’s the probability that a randomly selected dorm room has neither a TV nor a
refrigerator?
e)
What’s the probability that a randomly selected dorm room has a TV given that the
room had a refrigerator?
17.
Real Estate ads suggest that 45% of all homes have decks, 39% have patios and 14% have both.
a)
Create a Venn diagram with accurate values that represents this scenario.
b)
What percent of homes for sale have decks or patios?
c)
What percent have neither a deck nor a patio?
d)
What percent have a deck, but not a patio?
18.
A survey was done at Stone Bridge High School. 18% of all students have Play Station 2’s, 50%
have Wii’s, and 12% have both.
a)
Create a Venn diagram that represents this scenario.
b)
What percent of students have only Play Station 2’s?
c)
What percent of students have either Play Station 2’s or Wii’s, but not both?
d)
What percent of students do not have Wii’s?
e)
What is the probability of a student having a Wii given they have a Playstation 2?
19.
The table shows the political affiliation of American voters and their positions on the death
penalty. Don’t forget to write in totals for each category.
Republican
Democrat
Other
20.
Favor
0.26
0.12
0.24
Oppose
0.04
0.24
0.10
a)
What’s the probability that a randomly chosen voter favors the death penalty?
b)
What’s the probability that a Republican favors the death penalty?
c)
What’s the probability that a voter who favors the death penalty is a Democrat?
d)
A candidate thinks she has a good chance of gaining the votes of anyone who is a
Republican or in favor of the death penalty. What portion of voters is that?
You pick three cards at random from a deck of cards. Find the probability of each event
described below.
a)
You get no queens.
b)
You get all spades.
21.
22.
c)
The third card is your first black card.
d)
You have at least one diamond.
Your football team’s Regional Championship shirts have arrived in a big box, and people just
start grabbing them, looking for the right size. The box contains 14 medium, 20 large, and 16
extra-large shirts. You want a large for you, and one for your friend. Find the probability of
each event described.
a)
The first two you grab are the wrong sizes.
b)
The first large shirt you find is the third one you check.
c)
The first four shirts you pick are all extra-large.
d)
At least one of the four shirts you check is a large.
You pick five cards from a deck. What is the probability the five cards you pick are all clubs?
23.
Table of the number of males and females wearing jeans or not:
Males
Females
Total
Jeans
12
8
20
Other
5
11
16
Total
17
19
36
a)
Draw in a tree diagram to show percents. Round to the nearest thousandth.
b)
What is the probability that a male wears jeans?
c)
What is the probability that someone wearing jeans is male?
24.
The local SPCA shelter recently reported that it had 42 cats and 56 dogs. 22 of the cats are
female. All of the dogs are male.
a)
Draw a decision tree that represents the type and gender of pets at the SPCA:
b)
What percent of animals at the shelter are male dogs?
c)
What percent of animals at the shelter are female?
d)
What percent chance is there that you pick a female given that you are looking only at
cats?