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Mathematics B30
Module 4
Assignment 7
Mathematics B30
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Assignment 7
Mathematics B30
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Assignment 7
Optional insert: Assignment #7 frontal sheet here.
Mathematics B30
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Assignment 7
Mathematics B30
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Assignment 7
Assignment 7
(40)
A.
Multiple Choice: Select the correct answer to complete each of the following
statements and place a check () beside the correct answer.
1.
If x  2 then 2 x 2 equals ***.
____
____
____
____
2.
a.
b.
c.
d.
8
8
4
4
The expression  3b  is equal to ***.
5
____
____
____
____
a.
b.
c.
d.
 15b 5
 3b 5
 243 b 5
243 b 5
5
3.
4.
1

The first three terms of an expansion of  x  2  are ***.
2

____
____
a.
b.
____
c.
____
d.
The middle term(s) in the expansion of 2 x  3 y  is(are) ***.
8
____
____
____
____
Mathematics B30
x 5  10 x 4  5 x 3
x 5  10 x 4  5 x 3
x5 5 4 5 3
 x  x
32 8
2
5
x
5
 x4  5x3
32 8
a.
b.
c.
d.
70  16  81 x 4 y 4
70 x 4 y 4
56  32  27 x 5 y 3
56 x 5 y 3 , 70 x 4 y 4
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Assignment 7
5.

The expansion of x  2
____
____
____
____
6.
7.
 5 2 x 4  20 x 3  20 2 x 2  20 x  4 2
 5 2 x 4  20 x 3  20 2 x 2  20 x  4 2
4 2
 2 x 4  40 x 3  160 x 2  80 x  32
____
a.
1 001 a 4 2 10
____
____
____
b.
c.
d.
 2 002 a 5 2 9
is ***.
2 002 a 5 2 9
 1 001 a 4 2 10
In an expansion of 2 x  3 y  , x 6 y 15 is found in the ***.
21
a.
b.
c.
d.
16th term
15th term
14th term
6th term
In an expansion of 2 x  y  the coefficient of x 4 y 5 is ***.
9
a.
b.
c.
d.
 126
126
2 016
 2 016
In an expansion of  x  3 
12
____
____
____
____
Mathematics B30
is ***.
14
____
____
____
____
9.
x5
x5
x5
x5
5
The 10th term in an expansion of a  2 
____
____
____
____
8.
a.
b.
c.
d.

a.
b.
c.
d.
the coefficient of x 9 is ***.
220
 220
 5 940
5 940
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Assignment 7
10.
11.
The value of

____
____
____
____
 9  4 2i
 7  4 2i
3
1
is ***.
are ***.
a.
b.
c.
d.
i  17 x  136 ix 2  680 x 3
i  17 x  136 ix 2  680 x 3
1  17 x  136 x 2  680 x 3
 1  17 x  136 x 2  680 x 3
If a coin is tossed, and then a six sided die is rolled, and then a card is
drawn from a deck of 52 playing cards, to find the number of different
possible outcomes you use ***.
a.
b.
c.
d.
a Venn diagram
the binomial expansion
the first principle of counting
the second principle of counting
A contains 56 elements, B contains 38 elements, and 15 elements belong
to A  B . The number of elements in A  B is ***.
____
____
____
____
Mathematics B30
4
17
____
____
____
____
13.

The first 4 terms of the expansion of i  x 
____
____
____
____
12.
a.
b.
c.
d.
2 i
a.
b.
c.
d.
S
94
79
109
64
A
109
B
Assignment 7
14.
15.
If the odds that an event will happen are 2 to 5, the probability that the
event will not happen is ***.
____
a.
____
b.
____
c.
____
d.
The shaded region is represented by ***.
____
____
____
____
16.
17.
Mathematics B30
3
5
3
7
2
7
5
7
a.
b.
c.
d.
B  A C
B  A C
A  B C
A  B C
B
A
C
The number of distinct permutations of the letters of the word
“elements” is ***.
____
____
____
a.
b.
c.
____
d.
8!
8!3!
5!
8!
3!
Two dice are thrown. The probability that the sum of the numbers
showing is 4 or 7 is ***.
____
a.
____
b.
____
c.
____
d.
1
4
1
36
1
3
5
36
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Assignment 7
18.
19.
20.
Mathematics B30
Two cards are drawn from a deck of 52 playing cards. What is the
probability that either both cards are red or both cards are 10s?
____
a.
____
b.
____
c.
____
d.
55
221
16
663
357
1 326
681
1 326
Two marbles are drawn at random from a bag containing 4 red and 5
white marbles. Both marbles are selected in one draw. The probability
of selecting one red and one white marble is ***.
____
a.
____
b.
____
c.
____
d.
5
9
5
18
40
81
20
81
If, in Problem 19, the first marble is drawn and then replaced before the
second one is drawn, then the probability of selecting one red and one
white marble in the order, red first and white second, is ***.
____
a.
____
b.
____
c.
____
d.
5
9
5
18
40
81
20
81
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Assignment 7
Mathematics B30
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Assignment 7
Answer Part B and Part C in the space provided. Evaluation of your
solution to each problem will be based on the following.
(40)
B.
1.
Mathematics B30
•
A correct mathematical method for solving the problem is shown.
•
The final answer is accurate and a check of the answer is shown
where asked for by the question.
•
The solution is written in a style that is clear, logical, well
organized, uses proper terms, and states a conclusion.
A survey of students taking one or more courses of algebra, physics, and
statistics revealed the following numbers of students in the classes.
(A)
(P)
(S)
algebra 329
physics 186
statistics 295
a.
Draw a labelled Venn diagram showing the number in each
region.
b.
State the number of students in A  P  S .
c.
State the number of students in A  P  S .
algebra and physics 83
algebra and statistics 217
physics and statistics 63
physics, algebra and statistics 53
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Assignment 7
2.
Determine the probability that 10 tosses of a fair coin produce 5 heads
and 5 tails.
3.
Determine the probability that in a family of six children at least 4 of
them are boys.
4.
The probability that John will solve a certain problem is
will solve it is
a.
Mathematics B30
2
, that Mary
3
3
1
, and that Bill will solve it is .
4
2
Are these events dependent, independent, or mutually exclusive?
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Assignment 7
Mathematics B30
b.
What is the probability that all three will solve the problem?
c.
Draw a Venn diagram to illustrate the events and probabilities.
d.
What is the probability that John and Mary will solve it but Bill
will not?
e.
What is the probability that Mary and Bill will solve it but John
will not?
f.
What is the probability that John and Bill will solve it but Mary
will not?
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Assignment 7
5.
6.
Mathematics B30
g.
What is the probability that at least one of them will solve it?
h.
What is the probability that exactly one of them will solve it?
A bag contains 5 red marbles and 4 yellow marbles. One marble is
chosen at random from the bag and then, without replacing the first
marble, another marble is chosen from the bag.
a.
What is the probability that the marbles chosen will be of a
different color?
b.
If three marbles are chosen in this way, without replacement,
what is the probability that the first two are red and the last one
is yellow?
A family has two children. Assume that the probability of having a boy
is equal to that of having a girl.
a.
List all the elements of the sample space.
b.
Find the probability that both children are boys if it is known that
one of the children is a boy.
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Assignment 7
7.
(20)
C.
1.
A pair of dice is tossed. Let E be the event that the sum is 6. Let A be
the event that a 2 appears on at least one die. List the elements in each
event shown below and find each of the probabilities.
a.
P E 
b.
P A 
c.
P A  E 
d.
P A / E 
e.
P E / A 
Recall that the coefficient of the rth term of the expansion of  x  y  is
made up of r  1 factors in each of the numerator and denominator.
n
n n  1 n  2     n  r  2 
1  2  3    r  1 
Suppose that n is not a positive integer. Use the same procedure to
expand the following as used in the case that n was a positive integer
and then simplify.
a.
Mathematics B30
Given 1  x  , write the next 3 terms. The first three are given.
1 1 x 0   11 1 2 x 1   11 2 2  1 3 x 2 


1
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Assignment 7
2.
1
1
into 1  x  and into the expansion you
2
obtained in a. Show that the expansion approximates the
binomial power.
b.
Substitute x 
c.
Write the next three terms of the expansion of 1  x 2 and
simplify.
 1  1 
1
    3
1
   1 
  
1
2
2 0
2


 1  x   2  2   1 2  x 2 
1 x 



 1  2 
 1 


 


 


1
Summary pages for Lesson 13 and Lesson 14.
100 
Mathematics B30
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Assignment 7