From the Conditional probability formula, if events A and B are conditionally independent given event C,
a) Yes, for A and Bᶜ guaranteed to be conditionally independent given C.
b) No, A and B guaranteed to be conditionally independent given Cᶜ.
Conditional probability represented by notation P(A|B) is read as the probability of event A occurring given that event B has occurred. We will use the definition of conditional probability and independent events to prove the required result. In conditional probability, we calculate the probability of an event and it is known that the other event has already occurred. The events A and B are conditionally independent for the given event C such that P( C) > 0 and P( Cᶜ ) > 0.
In case of independent, the probability of one event can't be effect the probability of a 2nd event, that is Probability of intersection of two events is product of individual probabilities
From the definition of conditional probability, for independent events A and B, P( (A∩B)| C) = P( A|C) P( B|C)
a) Using the properties of conditional probability, [tex]P( ( A∩B^c )| C) = P( A|C) P( B^c |C) \\ [/tex]
so, yes, A and B guaranteed to be conditionally independent given C.
b) Using the properties of conditional probability independent, P( (A∩B)| C) = P( A|C) P( B|C) but [tex]P( (A∩B)| C^ c ) ≠ P( A|C^c) P( B|C^c) \\ [/tex].
So, A and B are not guaranteed to be conditionally independent given Cᶜ.
Hence, the first statement is right but not second.
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Complete question:
4. suppose that events A and B are conditionally independent given event C. suppose that p(C) > 0 and p(Cᶜ ) > 0. (a) are a and bc guaranteed to be conditionally independent given c? justify your answer. (b) are a and b guaranteed to be conditionally independent given Cᶜ ? justify your answer.
Find the area of the parallelogram. Round to the nearest hundredth if necessary.
Answer:
1424.81 square meters
Step-by-step explanation:
20.21 m * 70.5m = 1424.805 square meters
So then you round it to the nearest hundredth so then..
1424.81 square meters
Step-by-step explanation:
A of a parallelogram = Base ×height
= 20.21×70.5= 1424.805m
nearest hundreth = 1424.81 m
Jazzy goes to bed 3 h after dinner.
Yesterday, she spent 1 1/2 h on her homework and 2/3 h on the telephone after dinner.
How much time does she have before bed time?
PLEASE SHOW YOUR WORK!!!
Answer:
It was easy
Step-by-step explanation:
11 x 2 = 22
3 x 2 = 6
22 x 6 = 132
The time Jazzy has before going to bed is [tex]\frac{5}{6}[/tex] hour
The first step to take in determining the answer is to add the hours she spent on various activities she did after dinner
Sum of activities done after dinner = hours spent on homework + hours spent on the telephone
[tex]1\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex]
[tex]1\frac{3 + 4}{6}[/tex]
= [tex]1\frac{7}{6}[/tex]
=[tex]2\frac{1}{6}[/tex] hours
Th second step is to subtract the total hours Jazzy spent on activities from the hours Jazzy has before going to bed after dinner
Time left before she goes to bed = time she has to go to bed after dinner - total hours spent before going to bed
3 - [tex]2\frac{1}{6}[/tex] hours = [tex]\frac{5}{6}[/tex] hour
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a right circular cylinder with a radius of 2.3cm and a height of 1.4cm has a total surface area of
Answer:
i think 6.44
Step-by-step explanation:
first the diameter is 4.6 then multiply the 4.6 with 1.4 and u obtaine 6.44 (note:iam not sure iam still in seven grade)
someone help me please quick?
if I'm not wrong the answer does seem to be 69
Eqiuvalent expressions
5(x)(x)(x)(x)
Answer:
5x^4
Step-by-step explanation:
PLEASE PLEASE HELP ME!!!
Answer:
majadoxkdkdkrjjdkaoxjxjdhuriqwlsnxbxjdiirkekrnrnrjhfuxueiejhrhd2. Which of the following are solutions to - 2.7 + x = - 3.5?
Step-by-step explanation:
x = -4/5 = -0.8
Answer:
x = −0.8
Step-by-step explanation:
−2.7 + x = −3.5
1.) Simplify both sides of the equation
x − 2.7 = −3.5
2.) Add 2.7 to both sides
x − 2.7 + 2.7 = −3.5 + 2.7
AND BAYUM...
x = −0.8
~~~~~~~~~~~~~~~~~~~~~~~~~~~
Hope I helped!!!
GL :)
Find each angle measure.
Answer:
Step-by-step explanation:
1)140
2)70
x2 = 36 solve for x please answer
Step-by-step explanation:
Given
x² = 36
x² =( +6)²
x = +6
Hope it will help :)
Answer:
x= 18
Step-by-step explanation:
Divide both sides by 2
2 and 2 cancel out
36/2=18
check that it fits
2 x 18=36
18 is correct
Hope this helps ^-^
i need help with this pls 20 points for the right answer
Answer:
hiiii
Step-by-step explanation:
sorry I have not idea like what garde are u I'm
What are the possible measures of the triangle’s sides? Select all that apply.
Answer:
since a whole triangle is 180 you can do 60×3
Answer:
Step-by-step explanation:
Whole triangle = 180°
90 + 60 + 30
What is the main idea of this text
Atkins agreed to testify against Manson in exchange for avoiding the death penalty. Her grand jury testimony led to Manson being arraigned for the murders on Dec. 11, 1969. Atkins later recanted her testimony, and her deal was revoked by the prosecutors [source: Steffens and Staples]. Linda Kasabian, who hadn't entered any of the houses or committed any murders, was granted immunity and testified for the prosecution during the trial.
Answer:
the answer is Atkins agreeing to testify against Manson in exchange for avoiding the death penalty
find the perimeter of the rectangle
Answer:
b. 14 cm
Step-by-step explanation:
To find the other side of the right triangle, use the Pythagorean theorem, a^2+b^2=c^2. The side is 4 cm, so 3+3+4+4=14 cm.
Which equation does the model below represent? pls help !
Answer:
the answer to this is d
Step-by-step explanation:
x-3=5
a(b - 4) + c(b - 4)
can someone help me please!!!
Answer:
(b−4)(a+c)
Step-by-step explanation:
Answer:
ab-4a+cb-4c
Step-by-step explanation:
a(b-4)+c(b-4)
ab-4a+cb-4c
Which statement is true about the slope of the graphed line?
Answer:
B, the slope is positive.
Step-by-step explanation:
You can tell that the slope is positive because it is going upwards from left to right.
Solve the equation, and choose the type of solution you
found.
2x + 8 = 2(x + 4)
Answer:
All real numbers are solutions
Step-by-step explanation:
2x + 8 = 2(x + 4)
~Simplify right side
2x + 8 = 2x + 8
~Subtract 8 to both sides
2x = 2x
~Divide 2 to both sides
0 = 0
Best of Luck!
Answer: the answer is infinite
Step-by-step explanation: so first you need to distribute the 2 into the () and you would get 2x+8 and since it is the same on both sides it cancles eachother out therefore there is infinite answers
What is the value of w?
AnswThe letter (W) is the symbol used to represent whole numbers. Whole numbers are counting numbers from 0 to infinity. The whole numbers (W): 0, 1, 2, 3, 4 . . . Notice that every natural number is a whole number.er:
Step-by-step explanation:
Consider the equation: 1 4 x + 3y − 23 = 42 The variables are: The coefficients are: The constants are:
Answer:
The variables are: x and y
The coefficients are: 1/4 and 3
The constants are: -23 and 42
Step-by-step explanation:
Given equation:
1/4x + 3y − 23 = 42
The variables are: x and y
The coefficients are: 1/4 and 3
The constants are: -23 and 42
say something so mean to me idc just say whats on your mind broskis
Answer:
Can grape juice be made into grapes?
Your so UGLY you turned medusa into stone.
Step-by-step explanation:
I said what was on my mind
There are three rows of VIP seats in each section. Each row
has 12 seats and there are 16 sections. How many VIP seats
are there in all?
Answer:
576 I think
Step-by-step explanation:
3 x 12 x 16
Justin won the track event with a time of
12.0683 seconds. Write this round this off
to the nearest hundredth.
Answer:
12.068Step-by-step explanation: the nearest hundredth to 12.0683 is 12.068 because 3 is below five
Convert: 7 qt.=________fl.oz
Answer:
224 fl.oz
Step-by-step explanation:
Please help.
Is Algebra.
Answer:
5. 2, 6. 18
Step-by-step explanation:
8-?= 6, ? = 2
?-11 = 7, ? = 18
How many fluid ounces are in 1 quart
what is the solution to d · -4=32
Answer:
-8
Step-by-step explanation:
-4d=32
d=32/-4
d=-8
Which of the following could be the side measures of a right triangle? *
1)6 ft, 5 ft, 4 ft
2)8 ft, 7 ft, 6 ft
3)10 ft, 8 ft, 6 ft
4)12 ft, 10 ft, 8 ft
Answer:
option 1
Step-by-step explanation:
please Mark me as brainlist
The set of side lengths that could represent a right triangle is
12 ft, 10 ft, and 8 ft.
Option D is the correct answer.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
To determine which of the given sets of side lengths could represent a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
Using this theorem, we can check each of the given sets of side lengths to see if they satisfy this condition:
6 ft, 5 ft, 4 ft
6² + 5² = 36 + 25 = 61
4² = 16
Since 61 is not equal to 16, this set of side lengths does not represent a right triangle.
8 ft, 7 ft, 6 ft
8^2 + 7^2 = 64 + 49 = 113
6^2 = 36
Since 113 is not equal to 36, this set of side lengths does not represent a right triangle.
10 ft, 8 ft, 6 ft
10^2 + 8^2 = 100 + 64 = 164
6^2 = 36
Since 164 is not equal to 36, this set of side lengths does not represent a right triangle.
12 ft, 10 ft, 8 ft
12^2 + 10^2 = 144 + 100 = 244
8^2 = 64
Since 244 is equal to 64 + 180, this set of side lengths does represent a right triangle.
Therefore,
The set of side lengths that could represent a right triangle is 12 ft, 10 ft, and 8 ft.
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what is 69% of 69 what is 69% of 69
Answer:
69% of 69 is 47.61 :)
Using suitable identity find 5.62
− 0.32
Answer:
5.62 - 0.32= 5.3 or 5.30
Step-by-step explanation:
A box of dried fruit has 80 calories in 5 servings. How many calories are there per serving?
Answer:
16 calories per serving
Step-by-step explanation:
80/5=16 calories per serving
Answer:
16 calories per serving. Hope this helps
Step-by-step explanation: