Arthur has a box which contains 6 black balls and n (n ≥ 2) white balls, then at random, he takes 3 balls from the box. If the probability of taking any ball is the same and Pₙ is the probability of taking 1 black ball and 2 white balls, what is the largest possible value for Pₙ?
Answers
Answer:
11/68 or 0.1618Step-by-step explanation:
Balls
Black - 6White - nOptions of getting 3 balls
1. White, black, black2. Black, white, black3. Black, black, whiteProbability P(n) in each option
1. WBB
P(w) = 6/(n + 6)P(b1) = n/(n + 6 - 1) = n/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 1)P(n) =
P(w)P(b1)(P(b2) = 6/(n+6) × n/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)2. BWB
P(b1) = n/(n + 6)P(w) = 6/(n + 6 - 1) = 6/(n + 5)P(b2) = (n - 1)/(n + 5 - 1) = (n - 1)/(n + 4)P(n) =
P(b1)P(w)(P(b2) = n/(n+6) × 6/(n + 5) × (n - 1)/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)3. BBW
P(b1) = n/(n + 6)P(b2) = (n - 1)/(n + 6 - 1) = (n - 1)/(n + 5)P(w) = 6/(n + 5 - 1) = 6/(n + 4)P(n) =
P(b1)P(b2)(P(w) = n/(n+6) × (n - 1)/(n + 5) × 6/(n + 4) =6n(n - 1)/(n + 6)(n + 5)(n + 4)Final equation is same for each case:
P(n) = 6n(n - 1) / (n + 6)(n + 5)(n + 4)The easy way to find the maximum is to try the numbers or graph.
Both of the methods give the maximum integer n = 11 or n = 12
See attached graph
At both values n we get P(n):
P(11) = 6*11*10 / 15*16*17 = 11/68 = 0.1618 (rounded)P(12) = 6*12*11 / 16*17*18 = 11/68 = 0.1618 (rounded)
Related Questions
1. Line L passes through point (-1, 2) and (-3,-2) on a coordinate plane. Line
M passes through the points (1.1) and (-1, W). For what value of W will make
line L and line M parallel.
Answers
Answer:
Slope of a line passing through ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2} , y_{2}[/tex]) is given by:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Now,
Slope of line L, (m) = [tex]\frac{-3-(-1)}{-2-2}[/tex] = 0.5
Slope of line M, (n) = [tex]\frac{-1-1}{W-1}[/tex] = [tex]\frac{-2}{W-1}[/tex]
If the lines L and M are parallel to each other,
m = n
or, 0.5 = [tex]\frac{-2}{W-1}[/tex]
or, 0.5 (W - 1) = -2
or, W - 1 = -4
or, W = -3
Therefore the required value of W is -3.
The system of equations y = negative 3 x + one-half and y = one-fifth x minus 1 and four-fifths is shown on the graph below.
What is a reasonable estimate for the solution?
(0.7, –1.7)
(–1.7, 0.7)
(1.4, –3.3)
(–3.3, 1.4)
Answers
Answer:
the -1,17,0.7 but if i get it wrong i can give u free points
Step-by-step explanation:
Answer:
-1,17,0.7
Step-by-step explanation:
please help meeeeeeright now
Answers
The answer is 4 pairs.
Think of having x number of pairs, and $4.29x for the price of those pairs. 8.58 is standalone, so we focus on writing the equation:
[tex]8.58+4.29x=25.74\\4.29x=25.74-8.58\\4.29x=17.16\\\frac{4.29}{4.29}=\frac{17.16}{4.29} (division)\\x=4[/tex]
A bacon cheeseburger at a popular fast food restaurant contains 2,070mg of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?
Answers
x(86/100)=2070
and solve for x.
after you solve you will get; 2407 mg
so the recommended daily amount is 2407 my
Answer:
2,407mg of sodium is the recommended daily amount
Step-by-step explanation:
Using the cross multiplication you will get the answer.
1. make the problem as a fraction [tex]\frac{2070}{x} =\frac{86}{100}[/tex]
2. Cross multiply (2070*100=86*x)
3. Simplify the equation left. 207000 = 86x
2407 ≈ x (Divide both sides by 86)
a.
In 1983, a cast-iron pan cost $28.35. Today, a cast-iron pan costs $52.95. If the CPI is 166, what is the percent relation of the
actual price of a cast-iron pan to the expected price?
The actual price is 11.1% lower than the expected price.
The actual price is 20.8% lower than the expected price.
The actual price is 31.5% higher than the expected price,
d The actual price is 12.5% higher than the expected price.
b
C
Please select the best answer from the choices provided
Ο Α
B
O CO
OD
Answers
Answer:
D. The actual price is 12.5% higher than the expected price.
Step-by-step explanation:
hope i helped :)
Write value of each digit in 167.7
Answers
The 6 is 60
The first 7 is 7
The second 7 is 0.7
The place value of every digit in 167.7 is:
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7What is place value?Every digit in a number has a place value in mathematics. The value a digit in a number represents based on where it is in the number is known as place value. The place value of 7, for instance, is 700 or 7 hundred. The place value of 7,432 is 7,000, or 7,000, however.So, place the value of each digit of 167.7.
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7So, the place value of each digit is shown.
Therefore, the place value of every digit in 167.7 is:
167.7: 1 hundreds + 60 tens + 7 ones + 7 tenths167.7: 100 + 60 + 7 + 0.7Know more about place value here:
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Is the number 1.13 greater than, less than or equal to 1
Answers
Please help as soon as possible
Answers
Answer:
2.2.6
Step-by-step explanation:
1 1/5 - 1/3 =18/15 - ?
Answers
Answer:
25/66
Step-by-step explanation:
Evaluate each expression if k = -3, 55 - k
Answers
Step-by-step explanation:
=55-k
=55-(-3)
=55+3
=58
hope it helps.
Answer:58
Step-by-step explanation:
=55-(-3)
=55+3
=58
If you found my answer useful than mark me brainliest.
help due in 30 min!!!!!!!!!!!!!!!
Answers
Answer:
They have the same slope
Step-by-step explanation:
slope=4
Is 2/3 less than 2/8
Answers
Answer:
No
Step-by-step explanation:
If there is 2 pizzas and one i cut in tree slices and the other is cut in eight slices the 8 slices are goind to be smaller. Hope this helps
What is the answer to the problem?
30 = -5(m + 6) + m
Answers
30=−5(m+6)+m
Step 1: Simplify both sides of the equation.
30=−5(m+6)+m
30=(−5)(m)+(−5)(6)+m(Distribute)
30=−5m+−30+m
30=(−5m+m)+(−30)(Combine Like Terms)
30=−4m+−30
30=−4m−30
Step 2: Flip the equation.
−4m−30=30
Step 3: Add 30 to both sides.
−4m−30+30=30+30
−4m=60
Step 4: Divide both sides by -4.
−4m
−4
=
60
−4
m=−15
Answer:
m=−15
How many questions are in math map 7th grade
Answers
Answer:
It really depends how well you are doing. It varies from time to time. Mine was about 40-50 questions
Kara earns 12 cent for each paper she delivers. If she delivers papers to 42 customers each day, how much does she earn in 1 week ?
Answers
12x42=504
504 cents earned every day when 42 papers are delivered
For a week= 504x7
3528cents
Answer:
3,528 cents = 35 dollars and 28 cents
Step-by-step explanation:
She earns 12 cents for each paper delivered.
=> She earns: 12 x 42 = 504 cents a day
=> She earns: 12 x 42 x 7 = 3528 cents in 1 week.
That is probably the answer you're expecting.
But you shouldn't.
One customer might need more than 1 paper a day, so there's no clear answer to your question.
The cost to the store is $45. They will use a 35% markup. What is the selling price?
Answers
And the selling price is Cost + Markup
Therefore $45 + $15.75 = $60.75
What is the volume of a cone with a radius of 6 inches and height of 15 inches .
Answers
Answer:
565.49 inches cubed
Step-by-step explanation:
Answer:
V = approximately 565.49 in3
Give the ratio for tangent (0) in decimal form to 4 digits.
13
4
7.
Answers
Answer:
0.5714
Step-by-step explanation:
tan theta = perpendicular upon base that is P/B
P= 4
B= 7
P/B = 4/7 = 0.5714
The inequality 3x+2>x+8 is equivalent to:
A. x>3
B. x 32
D. x<−32
Answers
Answer:
x>3
Step-by-step explanation:
3x+2>x+8
-2 -2
3x>x+6
-x -x
2x>6
/2 /2
x>3
The solution of the inequality 3x+2>x+8 will be x>3. The correct option is A.
What is inequality?
When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that inequality is 3x+2>x+8. The inequality will be solved as below,
3x+2>x+8
3x>x+6
2x>6
x>3
Hence, the solution is x>3.
To know more about inequality follow
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Solve: 33 + 27 ÷ 9 + (30 ÷ 5)
Answers
Answer:
42
Step-by-step explanation:
You need to follow P--E--M--D--A--S
A X U I A U
R P L V D B
E O T I D T
N N I T I R
T E P I T A
H N L O I C
E T I N O T
S S C N I
I A O
S T N
I
O
N
An owner buys a used car for $9000. How much is the markup if the percent markup is 7%? Show your work or explain your reasoning to justify your answer.
Answers
Answer:
$9,630
Step-by-step explanation:
7% of $9000 is $630, so you just add $9000 and $630.
Please only 10% of people are smart to answer this
Answers
Answer:
it's the one highlighted in orange
Step-by-step explanation:
I hope this helps with your question :)
The inverse of F(x) is a function.
Answers
Answer:
Step-by-step explanation:
the word inverse refers to the opposite of another operation.
The inverse of the function f is denoted by f -1.
If you found my answer useful then mark me brainliest.
4(-3)(-2)
How do
I do this?
Answers
Answer:
4(-3)(-2) = 24
Step-by-step explanation:
first solve the numbers in parenthesis.
4(-3)(-2)
= 4(6)
the negative sign cancels out in the product, because both of the numbers you multiplied are negative, which makes the product positive.
now solve for 4(6).
4(6) = 24
A phone company charges for service according to the formula: C ( n ) = 29 + 0.04 n , where n is the number of minutes talked, and C is the monthly charge, in dollars. The slope in this equation is: ____________
The vertical intercept in this equation is: _____________
Answers
Hello!
Answer:Slope = 0.004
Vertical Intercept = 29.
Explanation:Basically, you can rearrange this equation so that is in the form of y = mx + b.
y = mx + b
C(n) = 0.04n + 29
The slope represents the rate of change of the cost per minute talked, and the 29 (vertical intercept) represents the monthly fee. The monthly fee will stay the same, however, the number of minutes talked is susceptible to change, hence the variable n represents it.
The graph shows the reciprocal parent function.
Which statement is true?
A. The function has no intercepts.
B. (1,1) is the x- and y-intercept of the function.
C. (0,0) is the x- and y-intercept of the function.
D. (0,1) is the x- and y-intercept of the function.
Answers
Answer:
A
Step-by-step explanation:
help pls I need help
Answers
Also sorry if it’s wrong
what is the equation of the line passing through the points (-4,-7) and (8,-13)
Answers
Answer:
y=5/3x-79/7
Step-by-step explanation:
(-4, -7)
x1 y1
(8,-13)
x2 y2
y2-y1/x2-x1=
13+7/8+4= 20/12= 10/6= 5/3
y=5/3x+b
-7=5/3(-4)+b
The equation of a line passing through the points (-4,-7) and (8,-13) will be x + 2y + 18 = 0.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
The given points are (-4,-7) and (8,-13).
Then the equation of a line passing through the points (-4,-7) and (8,-13) will be
[tex]\begin{aligned} y + 13 &= \dfrac{-13+7}{8+4} (x - 8)\\\\y + 13 &= - \dfrac{1}{2} (x - 8)\\\\2y + 26 &= -x + 8\\\\x + 2y + 18 &= 0 \end{aligned}[/tex]
More about the linear system link is given below.
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Can someone give me a 6 digit number stating with 4? I need this number for a project. Also it needs to be a random number.
Answers
Answer:
406789
Step-by-step explanation:
what does 20 times 90 equal
Answers
Answer:
1800
Step-by-step explanation:
Well the easiest way to do this is just do
9 x 2 = 18 and since in 20 and 90 there are two zeroes, add two zeroes at the end of 18!
Answer:
its equals 1,800
Step-by-step explanation: