Practice Week 3
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School
University of Maryland, College Park *
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Course
650
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
8
Uploaded by AlexaKCalderon
Practice week 3 - Results
Attempt 1 of Unlimited
Written Feb 28, 2024 12:30 AM - Feb 28, 2024 12:33 AM
Attempt Score
9 / 100 - 9 %
Overall Grade (Highest Attempt)
9 / 100 - 9 %
Question 1
0 / 8 points
Answer:
(0.16)
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A survey of students at a college found the following majors:
Accounting - 26
Finance - 9
Economic - 12
Management - 11
What is the probability that a random student selected is a Finance major?
State your answers using two decimal digits.
Divide the number of finance majors by the total number of students
Question 2
0 / 8 points
Answer:
(0.43)
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Question 3
0 / 8 points
Answer:
(0.43)
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A survey of students at a college found the following majors:
Accounting - 12
Finance - 8
Economic - 11
Management - 13
There were no dual majors. The majors are mutually exclusive. What is the
probability that a random student selected is a Finance or Economics major?
State your answers using two decimal digits.
Add the number of finance and economics majors and divide by the total
number of students
Events A and B are mutually exclusive. Suppose P(A)=0.38 and P(B)=0.05.
What is the probability of either A or B occurring?
Use two decimal digits.
Question 4
0 / 8 points
Answer:
(0.56)
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Question 5
0 / 8 points
Answer:
(0.0020)
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Question 6
0 / 8 points
P(A or B) = P(A) + P(B). The Simple Addition Rule
Events A and B are mutually exclusive. Suppose P(A)=0.29 and P(B)=0.15.
What is the probability that neither A nor B will occur?
Use two decimal digits.
P( not(A or B) ) = 1 - P(A or B) = 1- ( P(A) + P(B) ) = 1 - P(A) - P(B). This is the
Complement rule.
You flip a coin 9 times. What is the probability that all 9 flips are Heads?
Use 4 decimal digits.
P(H)^number of flips = 0.5^number of flips
30% of the cars in a dealer lot are red, 23% are black, and 24% are white. The
remainder are some other colors.
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Answer:
0
(0.0207)
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A salesperson randomly shows three cars to three different customers. A car
may be shown more than once because cars are selected randomly (The
salesperson is new).
What is the probability the first car shown was red, the second was black, and
the third was red again?
To be more clear, the first red car and the second red car (third car shown)
may be the same car. This is called sampling with replacement.
Use 4 decimal digits.
In sampling with replacement, the proportions or probabilities of red, black,
white, and "other" cars remain constant from sample to sample. When the
probabilities of a sequence of events remain constant from trial to trial, the
events are independent. In a Sequence of Trials of independent events, the
Simple Multiplication Rule applies. For a sequence of three trials, R=Red,
B=Black, P(RBR) = P(R) x P(B) x P(R).
For a more physical and intuitive example, let's do P(white, red, and black)
assuming there are 100 cars in the lot consisting of 40 red, 30 black, 20
white, and 10 other.
The first car is randomly selected. There are 20 ways in 100 that the
first car is white. After showing, it remains in the lot such that there are
40 red, 30 black, 20 white, and 10 other. The number of cars of each
color has not changed. The proportions or probabilities of events red,
black, white, and other are unchanged. The second car is randomly selected. There are 40 ways in 100 that the
second car is red. For each of the 20 ways in 100 that the first car is
white, there are 40 ways in 100 that the second car is red. How many
ways can the first and second color occur? It's 20 x 40 out of 100 x
Question 7
0 / 8 points
Answer:
0
(28,561)
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Question 8
0 / 8 points
Answer:
0
(15,180)
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100 ways. After showing the second car, it remains in the lot such that
there are still 40 red, 30 black, 20 white, and 10 other. The
proportions or probabilities of events red, black, white, and other are
unchanged.
Extending to the 3rd car shown, there are 20 x 40 x 30 out of 100 x
100 x 100 ways white, red, and black can occur. This is equivalent to =
0.20 x 0.40 x 0.30, which is the Simple Multiplication Rule.
For a dial-combination lock, how many different codes can be set with 4
dials and 13 numbers on each dial? This is equivalent to sampling 4 times
with replacement from 13 things (numbers) because numbers can repeat.
How many different code sequences of X numbers can be made from a lock
with Y numbers?
=Y^X
How many different card hands are there when drawing 3 cards without
replacement from a 46 card playing deck, which has no duplicate cards?
The Excel function for a combination is =COMBIN(N,n).
Question 9
9 / 9 points
Events A and B are independent if
Question 10
0 / 9 points
Answer:
0
(0.160)
P(B | A) ≠ P(B)
P(A and B) = P(A) x P(B)
Two Customers go into a shop independently.
Assume the following probabilities:
P(Customer makes a purchase) = 0.400
P(Customer does not make a purchase) = 1- 0.400
Compute the probability that both customers purchase (# purchases = 2) and
enter your answer with 3 decimal places.
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Question 11
0 / 9 points
Suppose we have probabilities:
P(Yes and Republican) is a ______ probability.
Question 12
0 / 9 points
Answer:
0
(0.176)
P(2 purchases) = P(Customer1 makes a purchase and Customer 2 makes a
purchase) =
P(Customer1 makes a purchase) x P(Customer2 makes a purchase) =
P(Customer makes a purchase) x P(Customer makes a purchase)
Joint
Conditional
Marginal
Suppose we know the following probabilities:
Republican Democrat Independent
Female
0.194
0.176
0.103
Male
0.197
0.056
?
What is the probability of event Democrat and Female. Enter the probability
with 3 decimal place accuracy.
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Done
The joint probability is located at the intersection of row Female and column
Democrat.