A total of 2n cards, of which 2 are aces, are to be randomly divided among two players, with each player receiving n cards. Each player is then to declare, in sequence, whether he or she has received any aces. What is the conditional probability that the second player has no aces, given that the first player declares in the affirmative, when (a) n = 2? (b) n = 10? (c) n = 100?
Answers
Answer:
\(P(X_s^c|X_F) =0.2\)
\(P(X_s^c|X_F) =0.31\)
\(P(X_s^c|X_F) =0.331\)
Step-by-step explanation:
From the given information:
Let represent \(X_F\) as the first player getting an ace
Let \(X_S\) to be the second player getting an ace and
\(\sim X_S\) as the second player not getting an ace.
So;
The probabiility of the second player not getting an ace and the first player getting an ace can be computed as;
\(P(\sim X_S| X_F) = 1 - P(X_S|X_F)\)
\(P(X_S|X_F) = \dfrac{P(X_SX_F)}{P(X_F)}\)
Let's determine the probability of getting an ace in the first player
i.e
\(P(X_F) = 1 - P(X_F^c)\)
\(= 1 -\dfrac{(^{2n-2}_n)}{(^{2n}_n)}}\)
\(= 1 - \dfrac{n-1}{2(2n-1)}\)
\(= \dfrac{3n-1}{4n-2} --- (1)\)
To determine the probability of the second player getting an ace and the first player getting an ace.
\(P(X_sX_F) = \text{ (distribute aces to both ) and (select the left over n-1 cards from 2n-2 cards}\)\(P(X_sX_F) = \dfrac{2(^{2n-2}C_{n-1})}{^{2n}C_n}\)
\(P(X_sX_F) = \dfrac{n}{2n -1}---(2)\)
\(P(X_s|X_F) = \dfrac{2}{1}\)
\(P(X_s|X_F) = \dfrac{2n}{3n -1}\)
Thus, the conditional probability that the second player has no aces, provided that the first player declares affirmative is:
\(P(X_s^c|X_F) = 1- \dfrac{2n}{3n -1}\)
\(P(X_s^c|X_F) = \dfrac{n-1}{3n -1}\)
Therefore;
for n= 2
\(P(X_s^c|X_F) = \dfrac{2-1}{3(2) -1}\)
\(P(X_s^c|X_F) = \dfrac{1}{6 -1}\)
\(P(X_s^c|X_F) = \dfrac{1}{5}\)
\(P(X_s^c|X_F) =0.2\)
for n= 10
\(P(X_s^c|X_F) = \dfrac{10-1}{3(10) -1}\)
\(P(X_s^c|X_F) = \dfrac{9}{30 -1}\)
\(P(X_s^c|X_F) = \dfrac{9}{29}\)
\(P(X_s^c|X_F) =0.31\)
for n = 100
\(P(X_s^c|X_F) = \dfrac{100-1}{3(100) -1}\)
\(P(X_s^c|X_F) = \dfrac{99}{300 -1}\)
\(P(X_s^c|X_F) = \dfrac{99}{299}\)
\(P(X_s^c|X_F) =0.331\)
Related Questions
I am struggling and I would be so happy if any of you helped me. Can someone help me with the last two red boxes please? The rest of the question is for reference to help solve the problem. Thank you for your time!
Answers
Answer:
I think you can go with:
The margin of error is equal to half the width of the entire confidence interval.
so try .74 ± = [ .724 , .756] as the confidence interval
Step-by-step explanation:
4. Maria also wants to study the relationship between the weight of puppies at birth
and their adult weight (at two years old). She collected data from five randomly
selected small-breed dogs and displayed the data in the table.
Birth weightAdult weight
(pounds) (pounds)
1.5 10
317
18
2.5 14
Birth weight Adult weight
(pounds) (pounds)
0.75 5
Part A. Use the data in the table to create a scatterplot. (5 points)
Part A.
(5 points)
Dog Birth and Adult Weights
Answers
Answer:
y = 4.87x + 2.28 Is the answer
Step-by-step explanation:
( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )
using a:
THE ULTIMATE LINEAR REGRESSION CACLAULTOR
yes it is the epic i get:
y = 4.87x + 2.28
Nothing more noting less ikr
y = 4.87x + 2.28 Being the answer
7. Suppose that the discriminating monopolist has the demand functions
P_{1} = 200 - 2Q_{1}; P_{2} = 180 - 4Q_{2} and that the cost function is C = 20(Q_{1} + Q_{2}) .
a) How much should be sold in the 2 markets to maximise profits?
b) What are the corresponding prices?
c) How much profit is lost if it becomes illegal to discriminate?
12 marks]
12 marks]
16 marks]
d) Discuss the consequences of the imposition of a tax of 5 per unit sold in market 1 by
Answers
a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.
b) The corresponding prices are $180 in market 1 and $160 in market 2.
c) If it becomes illegal to discriminate, the profit loss is $50.
d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.
a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.
In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.
For market 1:
MR₁ = dP₁/dQ₁ = -2
For market 2:
MR₂ = dP₂/dQ₂ = -4
Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:
MR₁ = -2 = dC/dQ₁ = 20
MR₂ = -4 = dC/dQ₂ = 20
Solving these equations, we find:
Q₁ = 10
Q₂ = 5
Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.
b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:
For market 1:
P₁ = 200 - 2Q₁ = 200 - 2(10) = 180
For market 2:
P₂ = 180 - 4Q₂ = 180 - 4(5) = 160
Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.
c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.
Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.
Under discrimination:
Profit = Total revenue - Total cost
For market 1:
Total revenue₁ = P₁ \(\times\) Q₁ = 180 \(\times\) 10 = $1
For market 2:
Total revenue₂ = P₂ \(\times\) Q₂ = 160 \(\times\) 5 = $800
Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600
Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300
Profit = Total revenue - Total cost = $2600 - $300 = $2300
Under non-discrimination:
Since the same price is charged in both markets, we take the average price:
Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170
Total revenue = Average price \(\times\) (Q₁ + Q₂) = $170 \(\times\) (10 + 5) = $2550
Total cost remains the same at $300.
Profit = Total revenue - Total cost = $2550 - $300 = $2250
Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.
d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.
This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.
The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.
The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.
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Alex has to pay his car insurance twice a year. Each Payment is 312. How much money should Alex budget for his insurance each month?
Answers
312 • 2 = 624
Step 2:
624 divided by 12 months
Answer:
$52 a month
Answer:
$52
Step-by-step explanation:
$52. Since Alex pays for car insurance twice a year, divide the cost of each payment by 6, the number of months in half a year. This will tell you how much money Alex needs to set aside each month to cover his insurance costs.
312÷6=52
QUESTION IN PICTURE
Please explain your answer in steps, thank you.
Answers
We can complete the blanks with the following ratios:
(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags
Since we do not need a flag at the starting line, then 32 flags will be required in total.
How to obtain the number of flagsTo solve the problem, we would first convert 400 yds to feet and miles.
To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.
To convert to miles, we would have 0.227 miles.
Now, we divide the entire race distance by the number of miles divisions.
This gives us:
7.5 mi /0.227 mi
= 33 flags
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Which parametric equations represent y = – |x|? Check all that apply.
WILL GIVE BRAINLIEST
HELPPPP
Answers
Answer:
C and E on edge
Step-by-step explanation:
The equations that correspond to the rectangular equation is option B, C, and E.
What are Parametric Equations?The equations in which the dependent and the independent variable are written in terms of an individual parameter are called Parametric Equations.
The rectangular equation is
y = -|x|
x = t² and y = –|t²|
x = 2t and y = –|2t|
x = t + 4 and y = –|t + 4|
These three equations will not change the original value.
It seems that your question is incomplete, the complete question is as follows:
x = –t and y = |–t|
x = t2 and y = –|t2|
x = 2t and y = –|2t|
x = t3 and y = |t3|
x = t + 4 and y = –|t + 4|
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Joe is asked to prove that the sum of the interior angles (, , and ) of the triangle he has drawn equals 180°. His triangle is represented in the diagram above, and his work is shown below.
Answers
The angles <1, <2, and <3 will not add up to 180 degrees. The angles <1 and <2 are alternate interior angles, and the angles <2 and <3 are also alternate interior angles, AB is parallel to CD.
What is angle sum property of triangle?The angle sum property of a triangle states that the sum of the interior angles of a triangle is always equal to 180 degrees. This means that if you measure the angles inside any triangle and add them up, the result will always be 180 degrees. This property holds true for all types of triangles, whether they are equilateral, isosceles, or scalene.
To understand this property, consider a triangle ABC with interior angles angle A, angle B, and angle C. If we draw a line segment from vertex A to a point D on side BC such that it is parallel to the side AB, then we can see that angle A and angle C are alternate interior angles of the parallel lines AB and CD. Similarly, angle B and angle C are alternate interior angles of the parallel lines BC and AD.
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A semi-circular transom above a 34 inch door is to contain a stained glass window. If the stained glass
window costs $1.40 per square inch, how much will the window cost?
Answers
The cost of the semi-circular transom stained glass window is $107.702.
What is defined as the semicircle?A semicircle is formed when a circle is divided in half along its diameter. The two halves are equal in size.
A semicircle, also known as a half-disk, is a circular sheet plate that has been folded in half. The semicircle has one line of symmetry, which is known as the reflection symmetry. Because the semicircle is half of a 360° circle, the semicircle's arc always measures 180°.Now, for the for given question;
The width of the door is given as 34 inch which is same as the diameter of the semicircle of window.
The radius of the window becomes 34/2 = 17 inches.
Now, the formula for the area of the semicircle is;
A = πr²/2
Where, r is the radius and π = 3.14.
Substitute the values;
A = (3.14)(17)²/2
On simplification
A = 76.93 square inch.
Now, the cost of window glass is $1.40 per square inch.
Thus, for 76.93 square inch.
Rate = 76.93×1.40
Rate = $107.702
Therefore, the cost of the semi-circular transom stained glass window is found to be $107.702.
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Amir is in charge of getting oranges for today's soccer game. He buys 2 bags with
6 oranges in each bag. He also buys 4 loose oranges.
Choose all the expressions that can be used to find the number of oranges Amir gets
in all.
Answers
The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all
What is linear expressions?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.
Let's represent the total no of oranges by x.
Therefore ,
2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.
an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x
x = 12+4 or x-12 = 4
= 16
therefore amir got 16 oranges in all
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The graph shows a translation of the function f(x) = |x|. What absolute value function is represented by the graph?
A V shape with vertex at negative 1 point 5 comma zero and passing through the points negative 2 comma 1 and negative 1 comma 1.
A. f(x) = |x| + 1.5
B. f(x) = |x| − 1.5
C. f(x) = |x − 1.5|
D. f(x) = |x + 1.5|
Answers
The absolute value function that is represented in the graph is f(x) = |x + 1.5| So the correct option is D.
What absolute value function is represented by the graph?The general absolute value function is:f(x) = |x|This absolute value function has a vertex at the point (0, 0). We know that the graphed function has a vertex at the point (-1.5, 0).
So basically we had a horizontal translation of -1.5 units or 1.5 units to the left. That is written as: g(x) = f(x + 1.5)
Replacing the absolute value function we get:g(x) = |x + 1.5|
Then the correct option is D.
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90×4/9=40 is this equation true
Answers
The equation is correct, and the value on both sides of the equation is 40.
To verify if the equation 90 × 4/9 = 40 is true, we can perform the calculation on both sides and compare the results.
On the left side of the equation:
90 × 4/9 = (90 × 4) / 9 = 360 / 9 = 40
On the right side of the equation:
40
Both sides of the equation evaluate to 40, which means they are equal. Therefore, the equation 90 × 4/9 = 40 is indeed true.
In summary, the equation is correct, and the value on both sides of the equation is 40.
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Help ASAP!
Question 1:
Check attached file for question 1
Question 2:
A new lake was populated with a small number of trout. The number of trout in the lake can be modeled by the function: P(t)=740 / 1+73e^−0.07 where t is the number of months since the population of trout was first introduced. Round all answers to the nearest whole number
A. what is P(0)= I got 10
B. What does the answer from part A tell us about the trout population?
C. How many trout were in the lake after 1 year?
D. How many trout were in the lake after 10 years?
E. lim t→∞P(t)= I got 740
F. What does the answer from part E tell us about the trout population?
Answers
The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
How solve the problem?A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.
B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.
C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.
D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.
E. lim t→∞ P(t) = 740, so the answer is 740.
F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.
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Lin lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil is 11 1/4 square inches. Its length is 4 1/2 inches. What is the width of the foil?
Answers
Answer: the answer is 2.5
Step-by-step explanation:
Answer:
w= 5/2 inches or 2 1/2 inches
Step-by-step explanation:
area = length × width (w)
45/4 = 9/2 × w
45/4 =9w/2
45×2 = 9w×4
90 = 9w×4
9w= 90/4= 45/2
w= 45/2 × 1/9
w= 5/2 inches or 2 1/2 inches
what does the 5 in 56.13 represent as a decimal
Answers
Answer: 50
Step-by-step explanation:
5 = Fifty
6 = Six
. = decimal
1 = One tenths
3 = Three hundredth
The graph shows the results of a survey that asked people to choose their favorite dinner foods. One of the persons surveyed is chosen at random What is the probability that she chose beef? Favorite Dinner Foods: Vegetables 8 ,Fish 10 ,Potatoes 6 ,Chicken 24 , pasta 14, beef 18
18%
17.5%
30%
22.5%
Answers
The probability that the person chose beef is:
18/80 = 0.225 = 22.5%
Therefore, the probability that the person chose beef is 22.5%. Answer: 22.5%.
The state of Colorado is 4 centimeters long and 3 centimeters wide on a map. A cartographer wants to use a scale factor of 2.5 to enlarge the map. What is the area of the enlarged map?
12 cm2
30 cm2
35 cm2
75 cm2
Answers
The area of the enlarged map is 75 cm². Answer: (D) 75 cm².
What is scale ?
Scale refers to the ratio of distances or sizes on a map or drawing to the actual distances or sizes of the objects they represent in the real world. It is often expressed as a ratio, such as 1:10,000 or 1/4 inch = 1 foot, and is used to create maps and drawings that accurately represent real-world objects and distances. Scales can be used to enlarge or reduce the size of a map or drawing, making it easier to view and work with.
The original area of Colorado on the map is:
Area = length x width = 4 cm x 3 cm = 12 cm²
To enlarge the map with a scale factor of 2.5, we need to multiply the length and width by 2.5:
New length = 4 cm x 2.5 = 10 cm
New width = 3 cm x 2.5 = 7.5 cm
The area of the enlarged map is:
New area = new length x new width = 10 cm x 7.5 cm = 75 cm²
Therefore, the area of the enlarged map is 75 cm². Answer: (D) 75 cm².
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Find the mode(s) for the following group of data items.
33, 30, 29, 28, 34, 31, 27, 29
Select the correct choice below and, if necessary, fill in the answer box within your choice.
O A. The mode(s) is/are
(Use a comma to separate answers as needed.)
O. B. There is no mode.
Answers
If you make 25 bookmarks and sell them each for 50 cents, if you sold all your bookmarks, how much money would you have?
Answers
Answer:
$12.50
Step-by-step explanation:
25 (bookmarks) x $0.50(price) = $12.50(profit)
Answer:
$12.50
Step-by-step explanation:
hope it hels u
plzz plzz plzz mark as brainliest
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
The value of the given summation is:
\(\sum (29a_i - 13b_i) ]= -30\)
How to find the sum?Here we know that the sums are:
\(\sum a_i = -10\\\\\sum b_i = -20\)
And we want to find the value of the sum:
\(\sum (29a_i - 13b_i)\)
First we can distribute the sum to get:
\(\sum 29a_i + \sum - 13b_i\)
And take the coefficients out of the sum:
\(29\sum a_i -13\sum b_i\)
Now replace the known values:
\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)
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Mr. Perez bought a living room showcase listed at 150,580 Pesos but discounted into 127,993 pesos. What was the rate of the discount?
Answers
Step-by-step explanation:
Mr. Perez bought a living room showcase listed at 150,580 Pesos but discounted into 127,993 pesos. What was the rate of the discount?
(150,580 - 127,993) / 150,580 = 15%
Solve the following system of equations by elimination. What is the value of x?
2x - 5y = 1
-3x + 2y= -18
Answers
6.3 + 5.8(4 − 3.5t) + 6.6t, when t = 2.
Answers
Answer:
2.1
Step-by-step explanation:
6.3 + 5.8(4 − 3.5(2)) + 6.6(2)
6.3+5.8(4−7)+(6.6)(2)
6.3+(5.8)(−3)+(6.6)(2)
6.3+−17.4+(6.6)(2)
-11.1+(6.6)(2)
−11.1+13.2
2.1
what is 11/2 times 1/3 as a fraction
Answers
Answer:
11/2 times 1/3 is 11/6
Step-by-step explanation:
11/2 times 1/3,
We have to multiply the numerators and denominators,
\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)
hence we get 11/6
HELP PLS!
Delta math
Answers
180-118=62
62=angle C
If angles C and A equal the same thing then you know what angle A is.
So, 62*2=124
Now do 180-124=56
How do i do this problem
Answers
Answer:
no clue
Step-by-step explanation:
Iskandar had 2433 marbles. He had 3 times as many marbles as Bruce. Tim had 235 fewer marbles than Bruce. How many marbles did Tim and Bruce have altogether?
I'll give you 10 pts if you give me the correct answer!
Answers
Graph the linear equation.
x = 6
Use the graphing tool to graph the linear equation.
Answers
The graph of the linear equation, x = 6, is shown in the image attached below.
How to Graph the Equation of a Vertical Line?The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.
Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.
Thus, the graph of the linear equation, x = 6, is shown in the image attached below.
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Choose the best multiple choice option below! Thanks in advance!
Answers
Answer:
Q5. D, Q6. D, Q9. B.--------------------
Question 5The range of the given function has one restriction, its denominator can't be zero, hence:
3x + 4 ≠ 0 ⇒ 3x ≠ - 4 ⇒ x ≠ - 4/3Therefore the function can get any value but zero:
y ≠ 0The matching answer choice is D.
Question 6Linear function is f(x) = mx + b.
Reciprocal of a function f(x) is 1/f(x).
So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).
The only answer choice in same form is D.
Question 9Substitute x = - 5/3 into function to get:
\(f(x)=\cfrac{1}{3*(-5/3)+5} =\cfrac{1}{-5+5} =\cfrac{1}{0}\)This is undefined value, therefore it represents the vertical asymptote.
The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).
Therefore the correct choice is B.
What is the simple interest if $1,000 is borrowed for 5 years at 5 % interest?
Answers
Step-by-step explanation:
A= $1250
Converting R percent to R a decimal
Liam sorted music albums in his collection into three genres as shown
Genre
Rock
Country
Holiday
Count
7
3
5
Which statements identify correct ratios for the album collection Select all that apply
The ratio of holiday music albums to the entire collection is 5:10.
The ratio of rock music albums to country music albums is 7 to 3.
The ratio of rock music albums to holiday music albums is 5 to 7
The ratio of country music albums to the entire collection is 1 to 5.
There is 1 holiday music album for every 3 albums in the collection