A lot of 1000 components contains 350 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective.
a. Find P(A).b. Find P(B|A) .c. Find P(A ∩ B).d. Find P(Ac ∩ B).e. Find P(B) .f. Find P(A|B).g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.
Answers
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
We have,
Given:
Total number of components (n) = 1000
Number of defective components (d) = 350
a.
P(A) is the probability that the first component drawn is defective:
P(A) = d/n = 350/1000 = 0.35
b.
P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:
Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.
P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349
c.
P(A ∩ B) is the probability that both the first and second components drawn are defective:
P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122
d.
P(\(A^c\) ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:
\(P(A^c)\) is the probability that the first component drawn is not defective:
\(P(A^c)\) = 1 - P(A) = 1 - 0.35 = 0.65
Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.
P(\(A^c\) ∩ B) = P(\(A^c\)) * P(B) = 0.65 * (350/999) ≈ 0.228
e.
P(B) is the probability that the second component drawn is defective:
P(B) = Number of defective components / Total number of components
= 350/1000
= 0.35
f.
P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:
P(A|B) = P(A ∩ B) / P(B)
= (0.35 * 0.349) / 0.35
= 0.349
g.
To determine if A and B are independent, we need to compare
P(A) * P(B) with P(A ∩ B).
P(A) * P(B) = 0.35 * 0.35 = 0.1225
P(A ∩ B) = 0.122
Since P(A) * P(B) = P(A ∩ B), A and B are independent events.
It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.
The occurrence or non-occurrence of A does not impact the probability of B.
Thus,
The probabilities are:
a. P(A) = 0.35
b. P(B|A) ≈ 0.349
c. P(A ∩ B) ≈ 0.122
d. P(A^c ∩ B) ≈ 0.228
e. P(B) = 0.35
f. P(A|B) = 0.349
g. A and B are independent.
Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).
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Related Questions
r = -7 and s = 7
please asnwer s - 5[r] =
Answers
The value of s-5[r] is 42.
What is subtraction?The process of subtracting one number from another is known as subtraction.
Given, r = -7 and s=7
s-5[r]
Substitute the values of s and r:
=7-5[-7]
=7+35
=42
Hence, the value of s-5[r] is 42.
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At a pancake breakfast, there are a total of 150 pancakes.
Some are blueberry, some are plain, some are chocolate chip.
Two-thirds of the blueberry ones are eaten.
Four-fifths of the plain ones are eaten.
Half of the chocolate chip ones are eaten.
Now there are an equal number of each type of pancake.
How many of each type of pancake was there to begin with?
Answers
Applying equations, the number of each type of pancake are originally: 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
How to Solve Word Problems Using Equations?Let's use the following variables to represent the number of each type of pancake:
Let x be the number of blueberry pancakes.Let y be the number of plain pancakes.Let z be the number of chocolate chip pancakes.From the problem statement, we know that:
x + y + z = 150 (total number of pancakes)
1/3 x blueberry pancakes are left
4/5 y plain pancakes are left
1/2 z chocolate chip pancakes are left
There are now an equal number of each type of pancake
From the last statement, we can set up the following equations:
1/3 x = y = 1/2 z
Multiplying all sides of each equation by the least common multiple of the denominators, we get:
2x = 6y = 3z
Dividing all sides of each equation by 2, we get:
x = 3y = 3/2 z
Now we can use the equation x + y + z = 150 to substitute for x in terms of y and z:
3y + y + 2/3(3/2z) = 150
Simplifying and solving for z, we get:
5z = 270
z = 54
Substituting z = 54 into x = 3/2 z, we get:
x = 81
Substituting z = 54 into y = x/3, we get:
y = 27
Therefore, there were originally 81 blueberry pancakes, 27 plain pancakes, and 42 chocolate chip pancakes.
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In the past month, Isabel rented 3 video games and 1 DVD. The rental price for each video game was$2.70 . The rental price for the DVD was $3.40. What is the total amount that Isabel spent on video game and DVD rentals in the past month?
Answers
Answer: $11.50
Step-by-step explanation:
g = video games rented
d = DVDs rented
3g + d = whatever
g = $2.70
d = $3.40
3(2.70) + 3.40 = $11.50
hailey is designing a counter top for her new kitchen and a diagram of this is on the grid below. area of the counter top is?
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Answer:
identify the figure of speech in thus line I'm in wonderful funeral
A tree was 60 inches tall. Three years later it was 105 inches tall
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Answer:
Im sorry but I think you have forgotten to pit your question innit
Answer:
Step-by-step explanation:
something is wrong with the question...
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What is the argument of Negative 5 StartRoot 3 EndRoot + 5 i?
Answers
Answer:
150 degrees
Step-by-step explanation:
correct on edge2020
Answer:
D on edge
Step-by-step explanation:
Find the radius of a circle with a diameter whose endpoints are (-7,1) and (1,3).
Answers
Answer:
r = 4.1231055
Step-by-step explanation:
So to do this, you need to find the distance between the two points:
(-7,1) and (1,3).
To do this, the distance or diameter (d) is equal to:
d = sqrt ((x2-x1)^2 + (y2-y1)^2)
In this case:
d = sqrt( (1 - (-7))^2 + (3 - 1)^2 )
d = sqrt( 8^2 + 2^2)
d = sqrt( 64 + 4)
d = sqrt( 68 )
The radius is half of the diameter, so:
r = 1/2 * d
r = 1/2 * sqrt( 68 )
r~ 4.1231055
Find the surface area of the figure
Answers
Answer:
122.30 cm²
Step-by-step explanation:
The figure is a triangular prism.
Formula for calculating surface area of a triangular prism = bh + L(S1 + S2 + S3)
Where,
b = 11 cm
h = 4.3 cm
S1 = 8 cm
S2 = 6 cm
S3 = 11 cm
L = 3 cm
Surface area = 11*4.3 + 3(8 + 6 + 11)
= 47.3 + 3(25)
= 122.3 cm²
The human body consist 1/10 hydrogen 16/25 oxygen 1/5 carbon
Answers
Answer:
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Step-by-step explanation:
Model the unknown number situation by writing an algebraic expression.
the difference of a number and one hundred
n-100
100 - n
n + 100
100 +n
Answers
Answer:
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Step-by-step explanation:
Answer: The answer you are looking for is A on edge
Step-by-step explanation: Pls Mark me Brainilist! I know that this is for sure Right!
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answers
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
follow the steps to find the area of the shaded region. 14 46 14
Answers
The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.
How to calculate the area of the sector?The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is
A = (θ/360) πr² sq. units
How to calculate the area of a triangle with an angle?The area of the triangle with measures of two sides and an angle between them is
A = 1/2 × a × b × sinC sq. units
Where a and b are the lengths of sides and ∠C is the angle between those sides.
Calculation:It is given that,
The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².
Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,
Area of the shaded region = Area of the sector - Area of the triangle
⇒ 78.6794 - 70.4956
⇒ 8.1838 cm²
Therefore, the required area of the shaded region is 8.1838 sq. cm.
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what percent of 20 is 18?
Answers
Answer:
90%
Step-by-step explanation:
A fraction consists of two numbers and a fraction bar:
18/20
The number above the bar is the numerator: 18
The number below the bar is the denominator: 20
Divide the numerator by the denominator to get fraction's value:
Val = 18 ÷ 20
Describe in words and symbols the end behavior of f(x)=−5x4
Answers
Answer:
The graph is attached below.
Step-by-step explanation:
Given the function
\(f\left(x\right)=-5x^4\)
Since the leading term of the polynomial (the term in a polynomial that contains the highest power of the variable) is -5x⁴, then the degree is 4, i.e. even, and the leading coefficient is -5, i.e. negative.
This means that f(x) → −∞ as x → −∞ and f(x)→−∞ as x→∞.
The graph is attached below.
Answer:
Step-by-step explanation:
Matteo makes raspberry punch. The table shows how many parts ginger ale and raspberry juice to use for a batch. Raspberry Punch Parts Ginger Ale 2 Parts Raspberry Juice 3 Matteo decides to add one part of raspberry juice. What is the new ratio of ginger ale to raspberry juice? 2 parts ginger ale to 3 parts raspberry juice 2 parts ginger ale to 4 parts raspberry juice 3 parts ginger ale to 3 parts raspberry juice 3 parts ginger ale to 4 parts raspberry juice
Answers
Answer:
Answer: There is 1 1/2 times more juice than ginger ale; there is 2/3 as much ginger ale as there is punch.
Step-by-step explanation:
Answer:
Answer A:
Step-by-step explanation:
2 parts ginger ale to 3 parts raspberry juice.
PLEASE HELP
The table of values represents an exponential function.
What is the y-coordinate of -3f(x-1) when x = 0
Enter your answer in the box.
SEE PHOTO
Answers
The y-coordinate of -3f(x-1) when x = 0 is -63
What is the y-coordinate of -3f(x-1) when x = 0From the question, we have the following parameters that can be used in our computation:
The table of values
So, we have
-3f(x - 1)
When x = 0, we have
y = -3f(0 - 1)
This gives
y = -3f(-1)
From the table, we have
y = -3 * 21
Evaluate
y = -63
Hence, the y-coordinate is -63
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Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Answers
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
\(\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}\)Step 3: Simplify the above equation
\(\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}\)Hence the equation of the circle is
\(x^2+y^2-10x+6y-15=0\)I need help solving the following equation. Please and thank you...
(3x^2+2x+1) - (-3x+x^2+4)
Answers
You expect to receive $10,000 at graduation in two years. You plan on investing it at 11% until you have $75,000. How long will you wait from now?
Answers
Answer:
about 19.31 years
Step-by-step explanation:
\(10000( {1.11}^{x} ) = 75000\)
\( {1.11}^{x} = 7.5\)
\(x ln(1.11) = ln(7.5) \)
\(x = \frac{ ln(7.5) }{ ln(1.11) } = 19.31\)
A box contains 2 red marbles, 5 green marbles and 8 blue marbles. Find the probability of the different events.
P ( 3 blue ) =
P (blue & green)
Answers
The value of the probability of the different events are,
The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
We have to given that;
A box contains 2 red marbles, 5 green marbles and 8 blue marbles.
Hence, Total marbles = 2 + 5 + 8 = 15
So, The value of the probability P (3) is,
⇒ 3 / 15
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/15 x 5/15
⇒ 8/15 x 1/3
⇒ 8 / 45
Thus, The value of the probability P (3) is,
⇒ 1 / 5
And, The value of the probability P (blue & green) is,
⇒ 8/45
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2x + 8 > -4. 2.find the solution set of x and express the solutions set in number form
Answers
The solution set of this inequality is {x| x > -6.1}
How to find the solution set?Here we have the inequality:
2x + 8 > -4.2
To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:
2x + 8 > -4.2
2x > -4.2 - 8
2x > -12.2
x > -12.2/2
x > -6.1
So the set of all numbers larger than -6.1, this in number form is:
{x| x > -6.1}
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find the output, y, when the input, is 5 y= 5x - 3
Answers
Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
Answers
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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HELP I WILL GIVE BRAINLIEST IF RIGHT
Answers
Answer:
a
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
I might be wrong but i'm pretty sure it's right
Ashe and her two friends will run a relay race. The length of the race is 4/6 mile. If each person runs the same distance, how far will Ashe run?
Answers
Answer:
Ashe will run 6 miles
Step-by-step explanation:
4/6 x 3/1 = 12/6 divided by 6 (for numerator and denominator) = 6/1 = 6
If m∠1 = 3x + 15, m∠2 = 4x - 5, and m∠3 = 5y, find the value of y. *
Answers
Answer:
from the election of wine and decor is he going is nuryslam is he going
Step-by-step explanation:
eye on r and I have to go back and I have to khow hasgot is he still is a good time for me e and decor ☺️ and I have to do some research is a good idea for you khow
Please Help. Functions and Relations. Which statement describes the function graphed?
Answers
In general, we say that a function is negative on an interval if
\(f(x)<0,x\in Interval\)In our case, notice that the minimum point of the graph is at (0,0); thus, the function is never negative.
The answer is option A, the function is never negative.Is 5/11 closer to 0, 1, 1/2
Answers
Answer:
If your rounding up, its 1/2
Step-by-step explanation:
Find the slope of a line parallel to -5y + 2 = 3x ?a. -3/5b. -5/3C. 3/5d. 5/3
Answers
Subtracting 2 from the given equation we get:
\(\begin{gathered} -5y+2-2=3x-2, \\ -5y=3x-2. \end{gathered}\)Dividing by -5 we get:
\(\begin{gathered} \frac{-5y}{-5}=\frac{3x}{-5}-\frac{2}{-5}, \\ y=-\frac{3}{5}x+\frac{2}{5}\text{.} \end{gathered}\)The above equation is in slope-intercept form, therefore, the slope of the given line is:
\(-\frac{3}{5}\text{.}\)Now, recall that two lines are parallel if they have the same slope.
Answer: Option a.
Joe paid $14.00 for a board game. This is 70% of the original price. What was the original price?
Answers
Answer:
69.99
Step-by-step explanation:
Answer:
23.80
Step-by-step explanation: