"if n balls are distributed randomly into k urns, what is the probability that the last urn contains j balls?"
Answers
The answer relies on whether the balls are different or not. If they are not, which is almost certainly what is intended.
If they are, the perceptive is a bit different. Your expression gives the likelihood that a particular set of j balls goes into the last urn and the other n−j balls into the other urns. But there are (nj) different possible sets of j balls, and each of them the same probability of being the last insides of the last urn, so the total probability of completing up with exactly j balls in the last urn is if the balls are different.
See attached file for the answer.
To calculate the probability that the last urn contains j balls when n balls are distributed randomly into k urns, consider the number of ways to distribute the balls among the k-1 urns and multiply it by the probability of the last urn containing j balls.
Explanation:To calculate the probability that the last urn contains j balls, we need to consider the number of ways to distribute the n balls among the k-1 urns (excluding the last urn) and multiply it by the probability of the last urn containing j balls.
Let's assume that the number of ways to distribute the n balls among the k-1 urns is denoted by C. The probability of the last urn containing j balls is then given by P(j) = C * (1/k).
For example, if there are 10 balls distributed randomly into 4 urns and we want to find the probability that the last urn contains 3 balls, we need to calculate the number of ways to distribute the 10 balls among the first three urns (C) and multiply it by the probability of the last urn containing 3 balls (1/4).
Related Questions
gregs gas station sells three different kinds of gasoline:regular,plus,and premium
mr.adams spent $36.25 on 12.5 gallons of regular gasoline at gregs gas station.determine the cost per gallon for regular gasoline,showing each step in the process.
Answers
36.25/12.5 = $2.90
Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline. To find the cost per gallon, divide the total cost by the number of gallons, resulting in a cost of $2.90 per gallon of regular gasoline at Greg's gas station.
To determine the cost per gallon for regular gasoline, we need to divide the total amount spent by Mr. Adams at Greg's gas station by the number of gallons of gasoline he purchased. In this case, Mr. Adams spent $36.25 on 12.5 gallons of regular gasoline.
Step-by-step calculation:
Write down the total cost of gasoline: $36.25.
Write down the total gallons of gasoline purchased: 12.5 gallons.
Divide the total cost by the number of gallons to find the cost per gallon: $36.25 \/ 12.5 gallons.
Perform the division: $36.25 \/ 12.5 gallons = $2.90 per gallon.
Therefore, the cost per gallon for regular gasoline at Greg's gas station is $2.90.
16x+x =12 solve justify each step with algebraic property
Answers
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6
16x + x = 12
17x = 12 <-- Combine like terms
x = [tex]\frac{12}{17}[/tex]
So, x is equal to 12/17 or approximately to 0.7.
99 POINTS POSSIBLE!!!! I have a lot of math problems.....Please show your work also:) I will give Brainiest too!
1.Chase picked three buckets of blackberries that weigh: 2.79 pounds, 2.45 pounds, and 2.62 pounds. What is the average weight for the three buckets?
2. Ashley is baking cookies for math class. The recipe calls for 4 4/5 cups of flour. Ashley has to make 1 1/3 times the recipe to feed the whole class. How much flour does Ashley need?
3. Jordan finished her homework in 1 1/2 hours. It took Kasey 3/4 an hour longer than Jordan to finish her homework. How long did it take Kasey?
4. 32.5 divided by -0.08
5. 4.3x= 81.7 (Decimal Equation)
Thank you for helping me if you did!!!!!!!! I really appreciate it very much!!!!!!!
Answers
average weight=(2.79+2.45+2.62)÷3
=2.62
2) recipe calls for 4 4/5=4+(4÷5)
=4.8
1 1/3=1+(1÷3)=4/3
So 4.8 times 4/3=6.4
3) Jordan took 1+1/2=1.5 hours
Kasey 3/4 an hour longer than Jordan
So Kasey took 1.5+(3÷4)=2.25 hours
4) 32.5÷(−0.08)=−406.25
5) 4.3x= 81.7
Solve for x by dividing both sides by 4.3 to get
X=81.7÷4.3
X=19
Hope it helps!
Hello!
1) 2.62
2) 4.8
3) 6.4
3) 2.25 hours
4) −406.25
5) X=19
I hope it helps!
Write 720,080 in expanded form with exponents
Answers
there are no exponents
hope this helps
What is 160,656 rounded to the nearest ten thousandth?
Answers
The nearest two ten thousands would be 160,000 and 170,000
160,656 is 656 away from 160,000, and 9,344 away from 170,000.
It is much closer to 160,000 than 170,000.
Differentiate
y=(6x)/(1-cot(x))
Answers
Can someone please help I need a clear explanation on how to solve this equation.
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
Answers
n = amount of students who chose lion
t = amount of students who chose tiger
so.. "t" chose tiger, ok
"Four times as many students chose Bulldog as chose Tiger"
namely, if "t" chose tiger, then 4 times that many chose Bulldog, thus
b = 4t
"Twice as many students chose Lion as chose Tiger"
namely, if "t" students chose tiger, twice as many chose lion
n = 2t
now, we know a total of 273 students were surveyed, thus
[tex]\bf \begin{cases} b+n+t=273\\ \boxed{4t}+\boxed{2t}+t=273 \end{cases} \\\\\\ 7t=273\implies t=\cfrac{273}{7}\impliedby \textit{that many chose \underline{tiger}}[/tex]
Answer:
78 students chose lion.
Step-by-step explanation:
Let x students chose tiger.
Let y students chose bull dog.
Let z students chose lion.
Total students = 273
[tex]x+y+z=273[/tex] ....(1)
Four times as many students chose Bulldog as chose Tiger.
[tex]y=4x[/tex]
Twice as many students chose Lion as chose Tiger.
[tex]z=2x[/tex]
Substituting the values of y and z in (1)
[tex]x+4x+2x=273[/tex]
=> [tex]7x=273[/tex]
x = 39 (students who chose tiger)
We have to find students who chose Lion or z (defined above)
[tex]z=2x[/tex]
[tex]z=2(39)[/tex]
So, z = 78
Therefore, 78 students chose lion.
What is 1 more ten than 11?
Answers
your answer is 21
hope this helps
14-9x=-8(10+x) slove and show check
Answers
A violin student records the number of hours she spends practicing during each of nine consecutive weeks. 6.2 5.0 4.3 7.4 5.8 7.2 8.4 1.2 6.3 what is the interquartile range (iqr) for this data?
Answers
1.2 4.3 5.0 5.8 6.2 6.3 7.2 7.4 8.4
Interquartile range is given by upper quartile - lower quartile
Location of lower quartile = 1/4 of the data set
Location of upper quartile = 3/4 of the data set
Lower quartile = 1/4 of 9 = 2.25th (rounded down to 2nd value) = 4.3
Upper quartile = 3/4 of 9 = 6.75th (rounded up to 7th value) = 7.2
Interquartile value = 7.2 - 4.3 = 2.9
To calculate the interquartile range (IQR) of the data set, the ordered values are split by the median to find Q1 and Q3. The difference between Q3 and Q1 gives the IQR which is 2.65 for this data set.
The interquartile range (IQR) is the measure of the middle 50 percent spread in a data set and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the IQR for the provided data set (6.2, 5.0, 4.3, 7.4, 5.8, 7.2, 8.4, 1.2, 6.3), we first need to order the data from smallest to largest and then identify Q1 and Q3. Using the median to split the ordered data into two halves and finding the medians of these two halves gives us Q1 and Q3, and their difference gives us the IQR.
Ordered data: 1.2, 4.3, 5.0, 5.8, 6.2, 6.3, 7.2, 7.4, 8.4Median (also Q2): 6.2Lower half (for Q1 calculation): 1.2, 4.3, 5.0, 5.8Upper half (for Q3 calculation): 6.3, 7.2, 7.4, 8.4Q1: (5.0 + 4.3) / 2 = 4.65Q3: (7.4 + 7.2) / 2 = 7.3IQR: 7.3 - 4.65 = 2.65Find a ·
b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.
Answers
To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
Explanation:To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.
Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.
Tom jogged 3/5 mile on Monday and 2/6 mile on Tuesday how much farther did Tom joy on Monday then on Tuesday
Answers
What is 8.478 in expanded form
Answers
8+0.4+0.07+0.008
The expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
Given:
The given number is [tex]8.478[/tex].
To find:
The expanded form of the given number.
Explanation:
Write the given number as the sum of the place values of its all digits to find the expanded form of the given number.
[tex]8.478=8+0.4+0.07+0.008[/tex]
Therefore, the expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
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Toby is making a picture graph each picture of a book is equal to 2 books he read the row for month 1 has 3 pictures of books how many books did T
oby read during month 1
Answers
Toby read 6 books during the first month by using the picture graph where each picture represents 2 books.
To determine how many books Toby read during month 1, follow these steps:
Understand each picture of a book represents 2 books read.Observe that Toby has 3 pictures of books for month 1.Multiply the number of pictures by the number of books each picture represents: 3 pictures * 2 books per picture = 6 books.Toby read 6 books during the first month.
at 7 p.m. last night, the temputure was 10 degrees. At 7 a.m. the next morning, the temputure was -2 degrees. By how much did the temputure change From 7 p.m. to 7 a.m.
Answers
10 to 0 =10
0 to -2 = 2
10+2 =12
it changed by 12 degrees
What is the square root of 25 over 36
Answers
for √25 =5
and √36= 6
hope this helps
A carpenter is making a brace for a chair. To do so she intersects two pieces of wood to make two sets of vertical angles. The ostuse angles formed are each 145 . What is the measurement of each acute angle formed
Answers
In this case, the angles will be divided into 4 and two of the adjacent angel will result in 180° if you add them. Then the answer to this question would be: 180°-145°= 35°
The acute angle formed will be 35°
Factor the expression completely:
2x² + 5x - 12
Answers
2x^2+5x-12
x^2+5x-24
(x+8)(x-3)
(x+8/2)(x-3/2)
(x+4)(2x-3)
Final answer: (2x-3)(x+4)
The Waist to Hip Ratio (WHR) is a ratio commonly expressed as a decimal that has been shown to be a good predictor of possible cardiovascular problems in both men and women. If Kevin has a WHR greater than 1, he is considered to be “high risk” for cardiovascular problems. Calculate Kevin’s WHR with a waist measurement of 42 inches and a hip measurement 2 inches less.
Answers
That means Kevin need to ease off on the sloppy joes.
Markia saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?
Answers
So multiply 270 by .35 and you woild get $94.50
Then you take 270 and subtract it by 94.50 and you get 175.50.
So your answer would be $175.50.
Hope this helps!
Suppose that x is the age of a husband, and y is the age of his wife. if men always marry women who are 3 years younger than themselves, what is the equation for y (wife's age) as a function of x (husband's age)?
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Avery's class sold candy bars for a fundraiser. There were 20 bars in each box. Avery sold 4 boxes and an additional 8 bars. Express the total number of boxes that Avery sold as a mixed number. How many candy bars did Avery sell?
Answers
he solde 8 and 1/5 boxes
he sold 8(20)+4 or 160+4 or 164 candy bars
Answer:
she sold 4 2/5 boxes of candy bars.
In total, she sold 88 bars.
:))
Step-by-step explanation:
if bx-2=k then x equal
Answers
bx = k + 2
x = (k+2)/b
Hope this helps!
Celia bought a bag of 12 goldfish for $3. What is the cost of 1 goldfish?
Answers
we know that
Celia bought a bag of [tex]12[/tex] goldfish for [tex]\$3[/tex]
so
by proportion
Find the cost of [tex]1[/tex] goldfish
[tex]\frac{3}{12} \frac{\$}{goldfish} =\frac{x}{1} \frac{\$}{goldfish} \\ \\x=3/12 \\ \\x=\$0.25[/tex]
therefore
the answer is
The cost of one goldfish is [tex]\$0.25[/tex]
Celia will pay 0.25 dollars for 1 goldfish. The cost of 1 goldfish is $ 0.25
The Total number of goldfish purchased is 12.
Cost price for 12 goldfish is $ 3.
Let the price of 1 goldfish be x dollars.
Therefore,
[tex]\begin{aligned}x \times\$12&=\$3\\x&=\dfrac{3}{12}\\x&=0.25\end{aligned}[/tex]
Hence, the cost of 1 goldfish is 0.25 dollars.
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An acidophilus culture containing 150 bacteria doubles in population every hour. Predict the number of bacteria after 12 hours.
Answers
So 150(2)^12 = 614,400
15/16 is 1 sixteenth groups of what size
Answers
(15/16) / (1/16) = x
15/16 * 16/1 = x
15 = x <= 1/16 groups of 15...I think...my mind is trying to comprehend..lol
Help Please?? 12. Of the following, which one is an observational study? A. Asking hearing-impaired people to try a new style of earphone to get their opinion B. Comparing survival rates between treating bone cancer with surgery versus treating it with radiation C. recording the daily output of a balloon factory for 6 months D. polling people on their favorite color I believe it would be 'C', yes?
Answers
Option 'C' is an example of an observational study because it involves recording data without manipulation from the researcher, fitting the definition of observing the natural state or habits of a situation over time.
Explanation:You have correctly identified option 'C' as an example of an observational study. In an observational study, researchers merely observe and record data without manipulating or intervening in the study environment or subjects. Option 'C', which involves recording the daily output of a balloon factory for 6 months, fits this description as it simply measures and records data over time without any intervention from the researcher.
It is different from a controlled experiment where variables are manipulated to assess the effect of treatments, as in option 'B', which compares survival rates between different treatments for bone cancer. Similarly, options 'A' and 'D' involve asking for opinions, which might be part of a broader observational study but are not observational studies by themselves.
In summary, an observational study is characterized by the purposeful absence of manipulation by the researcher and is designed to observe the natural state or habits of the subject or situation being studied.
50779 divided by 590 equals
Answers
But, you can round this to equal 86.1.
The next train will arrive in 32 minutes and 30 seconds. In how many seconds will the next train arrive
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Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2, and a vertical shift up 3 units.
y =
(I don't have the option to use the characters "/" or "[tex] \pi [/tex]" so they must not be in the answer.
Answers
and the vertical shift will add 3 so its
sin 4x + 3
Hope this helps
Answer:
y = sin 4x + 3
Step-by-step explanation:
A sine function is represented as y = a sin(bx + c) + d
Given values in the question are a = amplitude = 1
period = π/2 = 2π/b
Vertical shift d = 3 units up.
Horizontal shift c = 0
Since 2π/b = π/2
[tex]b=\frac{2\pi }{\frac{\pi }{2}} =\frac{4\pi }{\pi }=4[/tex]
Now the sinusoidal function will be
y = 1. sin( 4x ) + 3
y = sin 4x + 3