Midterm 1
05.03.2021, 20:38
Dashboard / My courses / Probability-Lecture,Merged-Spring 2021 / 22 February - 28 February / Midterm 1
Started on Friday, 5 March 2021, 7:43 PM
State Finished
Completed on Friday, 5 March 2021, 8:10 PM
Time taken 27 mins 39 secs
Marks 7.00/7.00
Grade 100.00 out of 100.00
Question 1
Correct
Mark 1.00 out
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For three events:
P(A) = 0.1,
P(B) = 0.2,
P(C) = 0.3,
P(A∩ B) = 0.02,
P(A∩ C) = 0.03,
P(B ∩ C) = 0.06,
P(A ∪B ∪C )=0.49.
Then events A, B, C are:
Select one:
a. not enough information
b. independent
c. not independent !
Your answer is correct.
Question 2
Correct
Mark 1.00 out
of 1.00
A foreman for an injection-molding firm admits that on
23
of his shifts, he forgets to shut off the injection
50
machine on his line. This causes the machine to overheat, increasing the probability that a defective molding
1
3
will be produced during the early morning run from 20 to 20 . The plant manager randomly selects a
molding from the early morning run and discovers it is defective. What is the probability that the
foreman forgot to shut off the machine the previous night?
Answer:
23
32
!
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Midterm 1
Question 3
05.03.2021, 20:38
What is the probability that ALASKA can be rearranged so that all the A's are together ?
Correct
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of 1.00
Answer:
1
5
!
Question 4
Correct
Mark 1.00 out
of 1.00
In Nazarbayev University math club lottery 22 balls numbered 1 through 22 are placed in a machine that
randomly draws seven of them (order does not matter). If the 7 numbers drawn match the 7 numbers math
club member had chosen, that math club member wins $5000. However, if 6 out of 7 numbers match, then
math club member wins second prize of $100. What is the probability that you win the second prize if you
have only one lottery ticket?
Answer:
7·15·7!·15!
22!
Question 5
Correct
Mark 1.00 out
of 1.00
For two events A and B , P(A) =
!
1
21
and P(A) =
. If A and B are independent, then what is the probability
5
100
of P(A ∪ B) ?
Answer:
46
125
!
Question 6
Correct
Suppose that 15 people, including you and a friend, line up for a group picture. How many ways can the
photographer rearrange the line if she wants to keep exactly 3 people between you and your friend?
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Answer:
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Midterm 1
05.03.2021, 20:38
13!·2·11
!
Question 7
Correct
Mark 1.00 out
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A poll conducted by a potential presidential candidate asked two questions: (1) Do you support
the candidate’s position on taxes? and (2) Do you support the candidate’s position on homeland security? A
total of twelve hundred responses were received; six hundred said “yes” to the first question and four
hundred said “yes” to the second. If three hundred respondents said “no” to the taxes question and “yes” to
the homeland security question, how many said “yes” to the taxes question but “no” to the homeland security
question?
Answer:
500
!
◀ mock midterm
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