he prior probabilities for events A1 and A2are P(A1)=0.30 and P(A2)=0.70. It is also known that P(A1∩A2)=0. suppose P(B∣A2)=0.20 and P(B∣A2)=0.05. if eeded, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive? Explain your answer. (i) P(A1)+P(A2∣A2)(ii) P(A1)+P(A1)=1 (iii) P(A1∩A2)=0 (iv) P(A2)=P(A2∣A1) (b) Compute P(A1∩B) and P(A2∩B). P(A1∩B)=P(A2∩B)= (c) Comprite P(B). P(B)=(d) Apoiv bayes' theorem to compote P(A1∣θ) and P(A2∣θ). P(A1∣B)=P(Az∣B)=
Answers
(a) A1 and A2 are not mutually exclusive because the probability of their intersection, P(A1∩A2), is not equal to zero.
(b) To compute P(A1∩B) and P(A2∩B), we can use the formula:
P(A∩B) = P(A) * P(B|A)
For A1∩B:
P(A1∩B) = P(A1) * P(B|A1)
= 0.30 * 0.05
= 0.015
For A2∩B:
P(A2∩B) = P(A2) * P(B|A2)
= 0.70 * 0.20
= 0.140
Therefore, P(A1∩B) = 0.015 and P(A2∩B) = 0.140.
(c) To compute P(B), we can use the law of total probability:
P(B) = P(B|A1) * P(A1) + P(B|A2) * P(A2)
Given that P(B|A1) = 0.05, P(A1) = 0.30, P(B|A2) = 0.20, and P(A2) = 0.70, we can substitute these values into the equation:
P(B) = 0.05 * 0.30 + 0.20 * 0.70
= 0.015 + 0.140
= 0.155
Therefore, P(B) = 0.155.
(d) Applying Bayes' theorem, we can compute P(A1|B) and P(A2|B):
P(A1|B) = (P(B|A1) * P(A1)) / P(B)
= (0.05 * 0.30) / 0.155
≈ 0.097
P(A2|B) = (P(B|A2) * P(A2)) / P(B)
= (0.20 * 0.70) / 0.155
≈ 0.903
Therefore, P(A1|B) ≈ 0.097 and P(A2|B) ≈ 0.903.
To explain the results in more detail, let's summarize the information in a table:
| Event | Prior Probability (P) | Conditional Probability (P(B|A)) |
| A1 | 0.30 | 0.05 |
| A2 | 0.70 | 0.20 |
We know that A1 and A2 are not mutually exclusive because P(A1∩A2) = 0. The table also shows the conditional probabilities of event B given A1 and A2.
To compute P(A1∩B) and P(A2∩B), we use the formula P(A∩B) = P(A) * P(B|A). Plugging in the values from the table, we find P(A1∩B) = 0.015 and P(A2∩B) = 0.140.
Next, we compute P(B) using the law of total probability, which considers the probabilities of B given A1 and A2, as well as the prior probabilities of A1 and A2. In this case, P(B) is found to be 0.155.
Finally, applying Bayes' theorem, we can determine the posterior probabilities of A1 and A2 given
B. Using the formula P(A|B) = (P(B|A) * P(A)) / P(B), we calculate P(A1|B) ≈ 0.097 and P(A2|B) ≈ 0.903.
These results demonstrate how conditional probabilities and Bayes' theorem can be used to update prior probabilities based on new information, in this case, the occurrence of event B.
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Related Questions
Find the value of x.
Answers
Answer:
x=8
Step-by-step explanation:
90+18+9x=180
2. Use set builder notation to give a description of each of these sets.
a) {0, 3, 6, 9, 12}
b) {−3, −2, −1, 0, 1, 2, 3}
c) {m, n, o, p}
4. For each of these pairs of sets, determine whether the first is a subset of the second, the second is a subset of the first, or neither is a subset of the other.
a) the set of people who speak English, the set of people who speak English with an Australian accent
b) the set of fruits, the set of citrus fruits
c) the set of students studying discrete mathematics, the set of students studying data structures
Answers
a) {0, 3, 6, 9, 12}
Using set builder notation, we can describe this set as follows: {x | x = 3n, where n is a non-negative integer and 0 ≤ x ≤ 12}.
b) {−3, −2, −1, 0, 1, 2, 3}
Using set builder notation, we can describe this set as follows: {x | -3 ≤ x ≤ 3, x ∈ Z}, where Z represents the set of integers.
c) {m, n, o, p}
Using set builder notation, we can describe this set simply as {m, n, o, p}, since the elements are already explicitly given.
4.
a) The set of people who speak English is a subset of the set of people who speak English with an Australian accent. Every person who speaks English will also fall into the category of speaking English with an Australian accent, as speaking English is a prerequisite for having an Australian accent.
b) The set of citrus fruits is a subset of the set of fruits. Every citrus fruit, such as oranges, lemons, and grapefruits, is a type of fruit.
c) It is not possible to determine the subset relationship between the set of students studying discrete mathematics and the set of students studying data structures without additional information. These sets may have some overlapping elements or could be completely disjoint, depending on the specific students and their chosen courses.
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A car factory made 16 cars with a sunroof and 24 cars without a sunroof. What is the ratio of the number of cars without a sunroof to the total number of cars?
Answers
Answer:
3:5
Step-by-step explanation:
24:40
24 cars without sunroof
24+16=40
40 total cars
reduce the ratio of 24:40
12:20
6:10
3:5
the answer is 3:5
enter the correct letters in the boxes on the left with the negative statements on the right. apples make good pies. a seven is not a prime number. the sun is hot today. b a line doesn't contain at least two points. 3 2
Answers
The correct letters to enter in the boxes on the left are: b and d.
Enter the correct letters in the boxes on the left with the negative statements on the right.
apples make good pies. - False (a)
a seven is not a prime number. - False (b)
the sun is hot today. - True (c)
a line doesn't contain at least two points. - True (d)
To determine the correct letters in the boxes, we need to identify which statements are negative.
In statement (a), "apples make good pies," the statement is positive because it states that apples do make good pies. Therefore, the letter "a" should not be entered in the box on the left.
In statement (b), "a seven is not a prime number," the statement is negative because it states that a seven is not a prime number. Therefore, the letter "b" should be entered in the box on the left.
In statement (c), "the sun is hot today," the statement is positive because it states that the sun is hot today. Therefore, the letter "c" should not be entered in the box on the left.
In statement (d), "a line doesn't contain at least two points," the statement is negative because it states that a line does not contain at least two points. Therefore, the letter "d" should be entered in the box on the left.
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2x + 3y = -1
5r 2y = 12?
Answers
I need HELPPPP I'll mark you the brainliest!
Answers
B, x = 2
Step-by-step explanation:
Given the vertices of the image, and preimage of this right isosceles triangle, we can find the line of reflection by definitively understanding how reflections work. Given the preimage contains the points A(-1,1), B(1,-1), and C(-3,-1). And that the image contains the points A'(5,1), B'(3,-1), C'(7,-1). We can differentiate the corresponding points and apply them to the rules of a reflection. if figure Z is reflected over x = n,
than Z'(x,y) = Z(-x+2n,y). Logically, you can see that this pattern resembles all three coordinates for the transformation. i.e A'(5,1) = A(--1+2n,1) ; (1+2n,1) = (5,1) ; 1 + 2n = 5, 2n = 4, n = 2
we can prove this by using another point:
B'(3,-1) = (-1+2n,-1) = (-1 + 4, -1) = (3,-1)
Hopefully you understand,
Pls mark brainliest this took me a very long time.
Tally question.
Quite easy.
Pls help :)
Answers
Answer:
39/73
Step-by-step explanation:
Solve for the given variable.
3s - 17 = 19
Answers
Add 17 to both sides-
3s - 17 = 19
+17 +17
Now, divide both sides by 3-
3s/3 = 36/3
Which gives the answer of s = 12
hope this helps !! :)
The measure of an angle is 14.2°. What is the measure of its complementary angle
Answers
Answer:
75.8º
Step-by-step explanation:
The sum of complimentary angles is 90º
c + 14.2 = 90
Subtract 14.2 from both sides
c = 90 - 14.2
c = 75.8º
Sneak preview is a members only video rental store there is a 12.00$ initiation fee and a 5.00$ per video rental fee write a function to show the total cost, C, of renting m number of movies from this store
Answers
Answer:
12+5m=C
Step-by-step explanation:
This is the equation because 12 represents the original price whilst 5m represents the price of a video for example if you rent 2 videos 12+5(2)=22
An office manager buys 34 chairs for the new office. Each chair cost $205. What is the total amount the office manager pays for chairs?
Answers
Multiply the number of chairs by the price of the chair:
34 x 205 = 6,970
Total spent = $6,970
Use the function below to find F(-4).
F(x) = 2x
A. -16
B. 1/8
C. -8
D. 1/16
(ITS NOT -8)
Answers
A mermaid has a terrarium that measures 42 inches × 10 inches × 9 inches. She also has a box
that measures 3 inches × 3 inches × 3 inches. Every minute, the mermaid fills the box with sand
from her backyard and then pours the sand into the terrarium. How many minutes does it take the
mermaid to fill three-quarters of the terrarium with sand?
Answers
Answer:
105 minutes
Step-by-step explanation:
The volume of the terrarium is ...
V = LWH
V = (42 in)(10 in)(9 in) = 3780 in³
The volume of a box is ...
V = (3 in)(3 in)(3 in) = 27 in³
Then the number of boxes it takes to fill the terrarium is ...
(3780 in³)/(27 in³/box) = 140 boxes
The mermaid wants to fill it 3/4 full, so only needs 3/4 this number of boxes. That is 105 boxes. At the rate of 1 per minute, ...
it will take 105 minutes to fill 3/4 of the terrarium
Answer: It will take her 1 hour and 45 min
Step-by-step explanation:
Please help!
From the table what are the x and y intercepts in coordinate form?
Answers
Answer:
(0,3) is the x intercept
(3,0) is the y intercept
Step-by-step explanation:
When it has 0 that means its directly on the line, since x is 0 on (0,3) that means the line is crossing the x intercept
8. A computer application generates a sequence of musical notes using the function f(n) 6(16)", where n is the
number of the note in the sequence and f(n) is the note frequency in hertz. Which function will generate the same
note sequence as fon)?
A g(n) = 12(2)
B. H(n) – 6(2) n
C. P(n) = 12(4)2n
Dk(n) = 6(8)an
Answers
Applying an exponential property, it is found that the function that will generate the same note sequence as function f(n) is given by:
B. \(H(n) = 6(2)^{4n}\)
What is function for the note sequence?The function for the node sequence is defined by:
\(f(n) = 6(16)^n\)
A function that will the same note sequence as function f(n) has the same initial value of 6. Additionally, applying an exponential property, we have that:
\(H(n) = 6(2)^{4n} = 6(2^4)^n = 6(16)^n\)
Hence option B is correct.
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8. john is four times as old as his son. i john is 44 years old, how old is his son?
Answers
John's son is 11 years old.
We are given that John is four times as old as his son. Let's represent John's age as J and his son's age as S. According to the given information, we can write the equation J = 4S.
We also know that John is 44 years old, so we can substitute J with 44 in the equation: 44 = 4S.
To find the age of John's son, we need to solve this equation for S. We can do this by dividing both sides of the equation by 4:
44 ÷ 4 = (4S) ÷ 4
11 = S
Therefore, John's son is 11 years old.
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Suppose that for each firm in the competitive market for potatoes, long-run average cost is minimized at $0.6 per pound when 150 pounds are grown. The demand for potatoes is Q = 40,000/p. If the long-run supply curve is horizontal, then what would be the total consumer spending?
Answers
Answer:
Total consumer spending is 160
Step-by-step explanation:
Here , we are interested in calculating the total consumer spending.
In a long run perfect competition market, price interest with MC and minimum point of AC
Hence , P = AC
this means that Q = 40,000/P = 40,000/150 = 266.67 which is approximately 267 potatoes will be consumed
The total consumer spending is thus 267 * 0.6 = 160
Mindy is saving money. She started with $0. After 6 weeks, she had $90 saved.
Mindy is not sure exactly how much money she saved each week. She assumes that she saved money at a constant rate from when she started saving money through week 6
Answers
Answer: She mad $15 each week
Find the equation of the line that passes through (0, -3) and is parallel to
the line joining the points (9, 2) and (3, -5).
Answers
Answer:
y = \(\frac{7}{6}\) x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )
m = \(\frac{-5-2}{3-9}\) = \(\frac{-7}{-6}\) = \(\frac{7}{6}\)
• Parallel lines have equal slopes , so
m = \(\frac{7}{6}\) is the slope of the parallel line
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = \(\frac{7}{6}\) x - 3 ← equation of parallel line
Hey there!
\( \\ \)
Answer:\( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}\)
\( \\ \)
Explanation:To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be \( \: \sf{d_1} \: \) and the line that is parallel to \( \: \sf{d_1} \: \) be \( \: \sf{d_2} \: \) .
\( \sf{d_2} \:\) passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
\( \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} \)
\( \\ \)
⇒Subtitute the values :
\( \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} \)
\( \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}\)
\( \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} \).
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
\( \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} \)
\( \implies \sf{y = \bold{\dfrac{7}{6}}x + b} \) \( \\ \)
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line \( \: \sf{d_1} \: \). Now, replace y with -3 and x with 0:
\( \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)
Therefore, the equation of the line \( \: \bold{d_1} \: \) is \( \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} \)
\( \\ \)
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ASAPPPPPO due at 11:59pm
Answers
Answer:
Part 1 : 22
Part 2 : 34
Step-by-step explanation:
plz i want the answer
Answers
Answer:
Step-by-step explanation:
1. 3(5) plus 2 = 17
2. 2(5)^2 = 25(2) = 50
3. (5-2)^2 =3^2 = 9
X=5
y=2
then a: 3*5+2=17
b:2*5*5=50
c:5-2=3*3=9
a=17
b=50
c=9
help me please question in the picture
Answers
Answer:
Step-by-step explanation:
that should be a triangular prism.
Help me pls and thank you
Answers
just chose the last one 75% are stars
considerastandard normal random variable z. what is the value ofzif the area to the right ofzis 0.2643?
Answers
To determine the value of the standard normal random variable z for which the area to the right of z is 0.2643, we can use the standard normal distribution table or a statistical software.
The value of z corresponding to an area to the right of z can be obtained by subtracting the given area from 1 since the area to the right is complementary to the area to the left. Therefore, the area to the left of z would be 1 - 0.2643 = 0.7357.
By referring to the standard normal distribution table or using a statistical software, we can find the z-value associated with an area of 0.7357. In this case, the z-value is approximately 0.611, indicating that the value of z for which the area to the right is 0.2643 is approximately 0.611.
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Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75. Last week he ordered 4 pizzas and spent $41.50. Assume the price for each pizza is the same.
a) Does the pizza parlor charge a delivery fee? Explain.
b) Write an equation describing the total amount Luke spends, d, to get p pizzas delivered.
Answers
Yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Luke gets pizza delivered from the same local pizza parlor every Thursday. This week, he ordered 3 pizzas for his family and spent $32.75.
Last week he ordered 4 pizzas and spent $41.50.
Each pizza costs when ordered 3 pizzas
= 32.75/3 = $10.91
Each pizza costs when ordered 4 pizzas
= 41.50/4 = $10.37
Yes, the pizza parlor charges a delivery fee.
= (41.50+32.75)/(3+4) = 10.60
d = 10.60p
Thus, yes, the pizza parlor charges a delivery fee and the equation describing the total amount Luke spends, d, to get p pizzas delivered is d = 10.60p.
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what is the answer to 13+(-19)
Answers
Answer:
13+(-19)=13-19=-6 is your answer
Answer:
\(13 + ( - 19) \\ 13 -19 \\ = -6\)
PLS MARK ME BRAINLIEST
i will give u brainliest
Answers
Answer:
1 39 > 39 - 2
2 28 + 11 < 310
3 7 * 8 = 56
Hope this helps :)
Please mark me as Brainliest
HURRY PLEASE HELP ME WITH THESE PROBLEMS
Answers
Answer:
The first one is 1/2.
The second is there are no mistakes.
Step-by-step explanation:
It is easy for me.
Answer:
There are no mistakes in the second picture.
54318+21298=____+____=75600
Answers
Answer:
Step-by-step explanation:
OK so 54318+21298=75616.
So i divided 75600 by 2 and got 37800 as an answer. So that means that 37800+37800=75600.
determine the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown.
Answers
The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.
The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.
Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.
Let us denote this density as ρ.
Next, we need to find the volume of the paraboloid.
The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.
In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3
Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3
The next step is to find the x and y coordinates of the mass center of the paraboloid.
We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV
Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.
Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV
To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.
The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz
After evaluating this integral, we get:
z = (3/5) * h = (12/5) units
Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.
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