For each set of probabilities, determine whether the events A and B are independent or dependent.
Answers
Answer:
[tex]\fbox{\begin{minipage}{15em}a, d: A and B are not independent\\b, c: A and B are independent\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Apply the correct formula to check whether two events are independent or not
If the events A and B are independent, then:
P(A) x P(B) = P(A⋂B)
The formula of conditional probability:
P(A⋂B) = P(A|B) x P(B) = P(B|A) x P(A)
Step 2: Perform the calculation
a)
P(A) x P(B) = (1/6) x (1/4) = 1/24
P(A⋂B) = P(A|B) x P(B) = (1/5) x (1/6) = 1/30
=> P(A) x P(B) is not equal to P(A⋂B)
=> A and B are not independent.
b)
P(A) x P(B) = (1/2) x (1/4) = 1/8
P(A⋂B) = 1/8
=> P(A) x P(B) is equal to P(A⋂B)
=> A and B are independent.
c)
P(A) x P(B) = (1/2) x (1/6) = 1/12
P(A⋂B) = P(A|B) x P(B) = (1/2) x (1/6) = 1/12
=> P(A) x P(B) is equal to P(A⋂B)
=> A and B are independent.
d)
P(A) x P(B) = (1/3) x (1/6) = 1/18
P(A⋂B) = P(B|A) x P(A) = (1/2) x (1/3) = 1/6
=> P(A) x P(B) is not equal to P(A⋂B)
=> A and B are not independent.
Hope this helps!
:)
Related Questions
What is 3(4a−3)−(6a+5)? (Thank you to everyone for their hard work!)
Answers
Answer:
6a−14
Step-by-step explanation:
Answer:
[tex]=6a-14[/tex]
Step-by-step explanation:
[tex]3\left(4a-3\right)-\left(6a+5\right)\\\mathrm{Expand}\:3\left(4a-3\right):\quad 12a-9\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\\mathrm{Simplify}\:3\cdot \:4a-3\cdot \:3:\quad 12a-9\\=12a-9\\-\left(6a+5\right):\quad -6a-5\\=12a-9-6a-5\\\mathrm{Simplify}\:12a-9-6a-5:\quad 6a-14\\=6a-14[/tex]
I need help on this can someone help me thank you it’s geometry:)
Answers
=========================================================
How to get this answer:
The largest angle ABD is 90 degrees because of the small little angle square marker. Another clue is the notation [tex]BA \perp BD[/tex]. The upside down T symbol means "perpendicular", showing the lines BA and BD form a 90 degree angle. The pieces of the angle (ABC = 4x and CBD = 5x) must add up to 90 degrees, or else they wouldn't fit like a jigsaw puzzle.
--------
(angle ABC) + (angle CBD) = angle ABD
4x + 5x = 90
9x = 90 ... combining like terms
9x/9 = 90/9 ... dividing both sides by 9
x = 10
-------
If x = 10, then 4x = 4*10 = 40, which is the measure of angle ABC
If x = 10, then 5x = 5*10 = 50 is the measure of angle CBD
We see that ABC+CBD = 40+50 = 90
Awnser needed thank you!
Answers
Answer:
Step-by-step explanation:
I think 33°
Answer:
its 34 i think
Step-by-step explanation:
Can someone please help me??
Answers
Answer:
A∪B = {0,1,3,5,6,7,9}
A∩B = {3}
Step-by-step explanation:
A = {1,3,5,7}
B = {0,3,6,9}
Now
A∪B is a union (unity) of both sets
A∪B = {0,1,3,5,6,7,9}
Now
A∩B is the intersection(common elements) of both sets
A∩B = {3}
Answer:
Step-by-step explanation:
A ={1, 3 , 5 , 7}
B= {0, 3 , 6 , 9}
A U B is a set of all distinct elements that are in A or B
A U B = {0, 1 , 3 , 5 , 6 , 7 , 9}
A ∩ B is a set of all distinct elements that are in both A & B
A ∩ B = {3}
A. A worker with 1700 hours of training is paid $40 per month.
B. A worker who works 40 hours is paid $1700.
C. There are 40 workers who are paid $1700 per month.
D. A worker with 40 hours of training is paid $1700 per month
Answers
Answer:
d.
Explanation:
Look at the title of the categories in the chart. 40 is categorized under “hours of training,” meaning 40 hours of training. 1700 is categorized under “monthly pay.” Put the information together and it means $1,700 for 40 hours that month.
What is the simplified form of this expression?
Answers
Answer:
B. -7[tex]x^{2}[/tex] + 3x + 5
Step-by-step explanation:
(-3[tex]x^{2}[/tex] + x + 5) - (4[tex]x^{2}[/tex] - 2x)
-3[tex]x^{2}[/tex] + x + 5 - 4[tex]x^{2}[/tex] - 2x
Combine like terms
-3[tex]x^{2}[/tex] - 4[tex]x^{2}[/tex] = -7[tex]x^{2}[/tex]
x - -2x = x + 2x = 3x
5
-7[tex]x^{2}[/tex] + 3x + 5
I hope this helps :))
What is the domain of the function shown on the graph?
Answers
Answer:
Step-by-step explanation:
Looking at the arrows on the graph, it appears that as the graph keep growing UP unbounded, it also keeps growing to the left unbounded (to negative infinity, to be exact). Looking to the right, it appears that as the graph decreases unbounded (the y values keep getting smaller), the graph keeps growing in the x direct to positive infinity. So the domain is
- ∞ < x < ∞
Micah is a busy college student. He carries a full load of classes and works a full time job to support himself financially while in college. Last semester, his total number of hours between job and classes each week usually amounted to about 80 hours. He has decided that he cannot do so many hours each week this semester. He feels that he has to cut back to about 80% as many hours. If half of his hours are to be school hours, how many school hours will he spend each week this semester?
Answers
Answer:
32 school hrs in a week.
Step-by-step explanation:
The reduction percentage =
80 x 0.80 = 64 (hrs)
The distribution =
64/2 = 32hrs
Leshawn has $580 in a savings account that pays 3% interest.
How much interest will be earned in 5 years?
How much interest will be earned in 6 months?
Answers
Answer:
For 5 years $87
For 6 months $8.7
Step-by-step explanation:
To calculate the interests, we use the simple interest formula
Mathematically;
I = PRT/100
where P is the amount invested called the principal = $580
R is the rate = 3%
Time differs which may be 5 years or 6 months according to the question.
kindly note that 6 months is 0.5 year
For 5 years, we have
I = (580 * 3 * 5)/100 = $87
For 6 months, we have;
I = (580 * 3 * 0.5)/100 = $8.7
Which of the following reasons can be used to justify statement #3 in the proof?
A Given
B the vertical angel theorem
C the reflexive property of congruence
D SSS
Answers
c because it is accuet.
hope it helps
Option C . The reflexive property of congruence is the correct reason that can justify statement 3 . BD≅BD
What is the reflexive property of congruence?The reflexive property of congruence states that every side, every angle, every line segment and every shape is congruent to itself.
To prove that ΔABD is congruent to ΔCBD where given that
1.Line segment AB ≅ Line segment CB (Given)
2. Then we can write AD ≅CD ; Given : D is the mid point of AC
3. line segment BD ≅ Line segment BD , this is true by reflexive property of congruence which states that every line segment or side is congruent to itself.
BD can be considered as side of both the given triangles
Therefore, the reason that can justify statement 3 is option C.
Also, Learn more about the properties of congruence from the link below:
https://brainly.com/question/2039214
#SPJ5
i need help!How would i find the value of X?
Answers
NEED HELP ASAP! Arianna correctly simplified an expression. When she substituted \ into the simplified expression, the value was –4. Which could be Arianna’s original expression? One-sixth (negative 3 x minus 24) One-sixth (negative 5 x minus 8) One-sixth (negative 10 x minus 4) One-sixth (negative 12 x minus 16).
Answers
Answer:
(1/6)(-10x - 4) = -4
Step-by-step explanation:
(1/6)(-3x - 24) = -4
=> -3x - 24 = -4 x 6
=> -3x - 24 = -24
=> -3x = 24 - 24
=> -3x = 0
=> x = 0 (not 2) => Incorrect option
(1/6)(-5x - 8) = -4
=> -5x - 8 = -4 x 6
=> -5x - 8 = -24
=> -5x = 8 - 24
=> -5x = -16
=> x = 16/5 (not 2) => Incorrect option
(1/6)(-10x - 4) = -4
=> -10x - 4 = -4 x 6
=> -10x - 4 = -24
=> -10x = 4 - 24
=> -10x = -20
=> x = 2 => Correct option
(1/6)(-12x - 16) = -4
=> -12x - 16 = -4 x 6
=> -12x - 16 = -24
=> -12x = 16 - 24
=> -12x = 8
=> x = -3/4 (not 2) => Incorrect option
=> Option C is correct
Hope this helps!
Answer: C. One-sixth (negative 10 x minus 4)
Step-by-step explanation: On Edgenuity!!!!!!!!!!!!!
Medical statistics indicate that 20% of the population will have cancer in their lifetimes. A group of 12 babies is selected at random. a. What is the probability that exactly 5 in the group will get cancer in their lifetime? b. What is the probability that at least 5 will get cancer in their lifetime? Record the answer to four decimal places (x.Xxxx)
Answers
Answer:
a. 5.3%
b. 7.3%
Step-by-step explanation:
we have to:
n = 12
p = 0.2
q = 1 - 0.2 = 0.8
We apply the binomial formula:
p (x) = nCx * p ^ x * p ^ (n-x)
a. P (x = 5) = 12C5 * 0.2 ^ 5 * 0.8 ^ (12-5)
12C5 = 12! / (5! * (12 -5)!) = 792
P (x = 5) = 792 * 0.2 ^ 5 * 0.8 ^ (12-5)
P (x = 5) = 0.053
which means that the probability is 5.3%
b. P (x => 5) = 1 - p (x <5)
P (x => 5) = 1 - p (x <= 4)
P (x => 5) = 1 - [P (x = 0) + P (x = 1) + P (x = 2) + P (x = 3) + P (x = 4)]
P (x = 0) = 12C0 * 0.2 ^ 0 * 0.8 ^ (12-0) = 0.069
P (x = 1) = 12C1 * 0.2 ^ 1 * 0.8 ^ (12-1) = 0.206
P (x = 2) = 12C2 * 0.2 ^ 2 * 0.8 ^ (12-2) = 0.283
P (x = 3) = 12C3 * 0.2 ^ 3 * 0.8 ^ (12-3) = 0.236
P (x = 4) = 12C4 * 0.2 ^ 4 * 0.8 ^ (12-4) = 0.133
replacing:
P (x => 5) = 1 - [0.069 + 0.206 + 0.283 + 0.236 + 0.133]
P (x => 5) = 1 - 0.927
P (x => 5) = 0.073
Which means that the probability is 7.3%
How do you solve the inequality 2x-3<-52x−3<−5
Answers
Answer:
Idk it really hard to do
The area of a triangle garden can
be no more than 120 square
feet. The base of a triangle
is 16 feet in
lenght What
inequalitie describes the
possible heights, h, of the
triangular garden?
Answers
Answer:
0< h ≤ 15
Step-by-step explanation:
A = 1/2 * base * height = 1/2*16*h = 8h
A no more is ≤.
A ≤ 120
8h ≤ 120
h ≤ 15
0< h ≤ 15
Height should be more than 0 feet and no more than 15 feet.
The equation y-2=3(x+1) is written in point-slope form. What is the equation in slope-intercept form?
Answers
Our first step would be to distribute this 3 through the
parentheses to get 3x + 3 on the right side of the equation.
On the left bring down your y - 2 to get y - 2 = 3x + 3.
Next we would move the -2 to the right side of the
equation by adding 2 to both sides to get y = 3x + 5.
Now, this equation is written in slope-intercept form because
the y is by itself on the left side of the equation.
in fantasy football, Real Performance statistics from actual players are used to generate mock scores for Imaginary teams and virtual games. What kind of data source is this?
Answers
Answer:
[tex]\fbox{\begin{minipage}{8em}Option B: Survey\end{minipage}}[/tex]
Step-by-step explanation:
The data is collected from actual players, from real world, not simulation.
=> Option A-Simulation is incorrect.
The data is all collected subjectively from actual players, and has not been manipulated purposely, like in an experiment, yet.
=> Option C-Experiment is incorrect.
The data is collected subjectively and used directly to generate mock scores without any manipulation.
The data can be considered the results of survey.
=> Option B-Survey is correct
Hope this helps!
:)
Answer: Simulation
Step-by-step explanation:
I took the quiz
the __________ set is the set of elements under consideration
Answers
Answer:
SYNTAX PROPERTY
Step-by-step explanation:
Find the volume of the cone
Answers
Answer:
489.84 m3 es la respuesta
What is a reasonable product of 3 9/10× 4 1/5?
Answers
Answer: 16.38
Step-by-step explanation: I had this same math problem a while ago and got it right.
Answer:
hello 55
Step-by-step explanation:
(—5t^3+4t^2—t)—(8t^2+t)
Answers
Answer:
Step-by-step explanation:
What is the completely factored form of x3 – 64x?
Answers
Answer:
x( x-8)(x+8)
Step-by-step explanation:
x^3 - 64x
Factor out an x
x( x^2 -64)
This is the difference of squares x^2 -8^2 which is a^2 - b^2 = (a-b)(a+b)
x( x-8)(x+8)
Answer:
[tex]x(x - 8)(x + 8)[/tex]
Step-by-step explanation:
[tex] {x}^{3} - 64x \\ x( {x}^{2} - 64) \\ x( {x}^{2} - {8}^{2} ) \\ = x(x - 8)(x + 8)[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
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b
Х
What is the value of c?
4
4 units
a
с
0 5 units
Y
6 units
3
Z
O 7 units
Answers
c=5
The length c is the hypotenuse of the triangle WYZ, and the value of c is 5 units
How to determine the value of c?Considering the triangle WYZ, we make use of the following Pythagoras theorem
c² = 4² + 3²
Evaluate the exponents
c² = 16 + 9
Evaluate the sum
c² = 25
Take the positive square root of both sides
c = 5
This means that the value of c is 5 units
Read more about right triangles at:
https://brainly.com/question/2217700
#SPJ5
Reid's Hardware discounts all riding lawnmowers 6% to customers paying in cash. If Trey paid $1,278.75 in cash for a riding lawnmower, then what was the original price of the lawnmower?
Answers
Answer:
$ 1360.37
Step-by-step explanation:
Suppose we call the original price of the lawnmower x.
That means, to get a discount, the equation would be,
x * 1 - x * 6% = 1278.75
= (94/100) * x = 1278.75
= (47/50) * x = 1278.75
x = 1278.75 * 47 / 50
= 1360.37
Please help with this question
Answers
Answer:
the SSS similarity theorem
Step-by-step explanation:
The triangles are not indicated as being right triangles (even though we know they are), so we cannot use the HL theorem.
The ratios of corresponding sides are the same, so the applicable theorem is ...
the SSS similarity theorem
__
3/(3+6) = 4/(4+8) = 5/15 = 1/3 . . . the ratio of shorter sides to corresponding longer sides.
_____
Additional comment
You recognize the smaller triangle as a 3-4-5 right triangle, and notice that the larger triangle is 3 times that size. If angle C were marked as the right angle it is, then the HL similarity theorem could also be used.
select the equation that has a y-intercept value of 3
Answers
Answer:
The y-intercept is the point of which the graphed line passes through the y axis.
Step-by-step explanation:
First person to give me Brainliest wins the official contest!! Hurry!! Please give me Brainliest, I just started using this and really want it.
What is the name of this shape?
Please help!
Answers
Answer:
It is an isosceles triangle
Step-by-step explanation:
because there are 2 straight lines
Need Help. Order of operation 1/35 * 1/22 I get a different answer
Answers
Answer:
[tex]\frac{1}{770}[/tex]
Step-by-step explanation:
[tex]\frac{1}{35} *\frac{1}{22} =\frac{1}{770}[/tex]
Answer:
1 / 770.
Step-by-step explanation:
1/35 * 1/22
= 1*1 / 35*22
= 1 / 770.
Triangle ABC was transformed to be triangle DEF using one transformation. What transformation was performed? translation reflection rotation dilation
Answers
Answer:
This is a rotation of 180 degrees
Step-by-step explanation:
A translation is a shift side to side or up and down
A reflection is a mirror image across a line
A dilation is a shrink/enlargement
This is a rotation of 180 degrees. If we rotate around the origin 180 degrees, we will have the same image
Answer:
B. one 90 degree rotation
Step-by-step explanation:
im smart.
Plzzzzz i need help fast