If balls are randomly chosen from an urn containing red, white, blue, and green balls, find the probability that
Answers
The conditional probability that all four balls chosen are white, given that all balls are of the same color, is approximately 0.0893 or 8.93%.
To find the conditional probability that all four balls chosen are white, given that all balls are of the same color, we need to calculate two probabilities: the probability that all four balls are white and the probability that all four balls are of the same color.
The probability that all four balls are white can be calculated as follows:
P(All four balls are white) = (Number of ways to choose 4 white balls) / (Total number of ways to choose 4 balls)
Number of ways to choose 4 white balls = C(5, 4) = 5
Total number of ways to choose 4 balls = C(4+5+6+7, 4) = C(22, 4) = 7315
P(All four balls are white) = 5 / 7315
Now, let's calculate the probability that all four balls are of the same color.
We can calculate this probability for each color (red, white, blue, and green) and sum them up:
P(All balls are of the same color) = P(All four balls are red) + P(All four balls are white) + P(All four balls are blue) + P(All four balls are green)
To calculate the probability that all four balls are of a specific color, we use the same formula as before:
P(All four balls are of a specific color) = (Number of ways to choose 4 balls of that color) / (Total number of ways to choose 4 balls)
Number of ways to choose 4 balls of a specific color = C(Number of balls of that color, 4)
Total number of ways to choose 4 balls = C(4+5+6+7, 4) = 7315
Using this formula for each color, we get:
P(All four balls are red) = C(4, 4) / 7315 = 1 / 7315
P(All four balls are white) = C(5, 4) / 7315 = 5 / 7315
P(All four balls are blue) = C(6, 4) / 7315 = 15 / 7315
P(All four balls are green) = C(7, 4) / 7315 = 35 / 7315
Now we can calculate the conditional probability using Bayes' theorem:
P(All four balls are white | All balls are of the same color) = P(All four balls are white) / P(All balls are of the same color)
P(All four balls are white | All balls are of the same color) = (5 / 7315) / [(1 / 7315) + (5 / 7315) + (15 / 7315) + (35 / 7315)]
Simplifying the expression:
P(All four balls are white | All balls are of the same color) = (5 / 7315) / (56 / 7315) = 5 / 56 ≈ 0.0893
Therefore, the conditional probability that all four balls chosen are white, given that all balls are of the same color, is approximately 0.0893 or 8.93%.
Learn more about conditional probability click;
https://brainly.com/question/10567654
#SPJ4
Complete question =
If 4 balls are randomly chosen from an urn containing 4 red, 5 white, 6 blue, and 7 green balls, find the conditional probability they are all white given that all balls are of the same color.
Related Questions
Which polynomial represents the sum below?
3x? +7x+3
5x2 + 12x
+
O A. 15x2 + 19x+ 3
B. 8x2 + 19x+ 3
C. 8x2 + 84x + 3
O D. 15x2 + 84x + 3
Answers
Answer:
\(8x^2+19x+3\)
Step-by-step explanation:
\(3x^2+7x+3+5x^2+12x=\\3x^2+5x^2+7x+12x+3=\\8x^2+7x+12x+3=\\8x^2+19x+3\)
Answer:
i did it
Step-by-step explanation:
There are four typical measures of the central tendency of a frequency distribution. Which of the following is NOT ameasure of central tendency?a. meanb. medianC moded. method of least squares
Answers
method of least squares is not a measure of central tendency which is not involved in the typical measures.
The central tendency of the dataset are defined as three important measures namely mean, median and mode. The mean shows the average value of the dataset. which can be calculated as the sum of all the values in the dataset which are divided by the number of values. and it is considered as the arithmetic mean. Some of the other measures of mean which is used to find the central tendency are as mentioned as:
Geometric Mean , Harmonic Mean ,Weighted Mean.
Median is the middle value of the dataset in which the it is arranged in the ascending order or in descending order. When the dataset which contains an even number of values, then the median value of the dataset can be calculated by taking the mean of the middle two values.
The mode shows the frequently occurring value in the dataset. Sometimes the dataset are arranged and which contain multiple modes and in some situations , it does not contain any mode at all.
To know more about central tendency ,click here:
brainly.com/question/30218735
#SPJ4
a physical fitness association is including the mile run in its high school fitness test. mean 440 and a standard deviation of 60 seconds. longer than 302 second to run the mile
A. 0.9893
B. 0.4893
C. 0.0107
D. 0.5107
Answers
The probability that a student takes longer than 302 seconds to run the mile, given a mean of 440 seconds and a standard deviation of 60 seconds, is approximately A. 0.9893.
To calculate the probability, we need to find the area under the normal distribution curve that represents the students who take longer than 302 seconds to run the mile. We can use the standard normal distribution table or a calculator to find this probability.
First, we need to standardize the value 302 seconds using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, the standardized value is z = (302 - 440) / 60 = -2.3.
Next, we look up the corresponding area in the standard normal distribution table or use a calculator to find the probability associated with the standardized value of -2.3. The area to the left of -2.3 is approximately 0.0107.
However, we want the probability of the students taking longer than 302 seconds, which is the area to the right of -2.3. Since the standard normal distribution is symmetric, the area to the right is equal to 1 minus the area to the left.
Therefore, the probability that a student takes longer than 302 seconds to run the mile is approximately 1 - 0.0107 = 0.9893.
Hence, the correct answer is A. 0.9893.
To know more about probability refer here:
https://brainly.com/question/29062095#
#SPJ11
What is the length of the missing side, x?
40 in.
740
35 in.
510
49 in.
740
55°
х
Answers
Answer:
using similarity side 35 in. is similar to side x and side 40 in. is similar to side 49 in.
so... x\35in.=49/40
x×40=49×35
40x=1715
x=1715÷40
x=49
pls help i tried so many answers and none of them are right
Answers
Rectangle: 5*4=20square feet
Parallelogram: 5*2=10square feet
Trapezoid: 4*3=12square feet; 2*3=6 => 6/2=3square feet
20+10+12+3=45square feet
You’re welcome:)
what information can you gather from the standard deviation, particularly as it pertains to the percentage of normal distribution?
Answers
The standard deviation of a data set provides information about the spread or dispersion of the data around the mean.
It helps to determine the percentage of normal distribution in the data. If the standard deviation is small, it indicates that the data is tightly clustered around the mean and a high percentage of the data falls within a few standard deviations of the mean. On the other hand, if the standard deviation is large, it suggests that the data is more spread out and a smaller percentage of the data falls within a few standard deviations of the mean.
In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, the standard deviation provides insight into the proportion of data points that are close to the mean, and therefore, the shape of the distribution.
Learn more about Standard Deviation here:
https://brainly.com/question/475676
#SPJ4
What is the correct way to name the following image?
Answers
The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.
How do we name the vector diagram?
Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.
Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.
Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.
Learn more about vector diagram here: https://brainly.com/question/19802988
#SPJ1
show a general method for determining all the factors of a counting number in an efficient way. illustrate with the 150. explain how you have found all the factors
Answers
The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
One general method for determining all the factors of a counting number is by using the prime factorization method.
Here are the steps:
1. Start with the smallest prime number, 2, and divide the number by 2.
2. If the number is divisible by 2, write down 2 as a factor and divide the number by 2 to get a new number.
3. If the new number is still divisible by 2, repeat the process. If not, move on to the next smallest prime number, 3.
4. Continue this process with each prime number until you have fully factored in the original number.
Let's illustrate this method with the number 150:
1. 150 ÷ 2 = 75. So, 2 is a factor and our new number is 75.
2. 75 is not divisible by 2, so we move on to the next smallest prime number, 3.
3. 75 ÷ 3 = 25. So, 3 is a factor and our new number is 25.
4. 25 is not divisible by 3, so we move on to the next smallest prime number, 5.
5. 25 ÷ 5 = 5. So, 5 is a factor and our new number is 5.
6. 5 ÷ 5 = 1. So, 5 is a factor and our new number is 1.
We have now fully factored 150 into its prime factors: 2, 3, 5, and 5. To find all the factors of 150, we can multiply these prime factors in different combinations:
1 × 150 = 150
2 × 75 = 150
3 × 50 = 150
5 × 30 = 150
6 × 25 = 150
10 × 15 = 150
So, the factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.
To know more about factors refer here:
https://brainly.com/question/29128446#
#SPJ11
Please helpppp meeeee !!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answers
Answer:
The code will stop when x = 12
Step-by-step explanation:
The code loops until x is less than 12. X cannot be equal to 12 it has to be less than.
A membership at a health club costs $560 per year. The club has a payment plan in which a member can pay $50 down and the rest in 12 equal payments. How much would the monthly payment be?
Answers
If the club has a payment plan in which a member can pay $50 down and the rest in 12 equal payments, the monthly payment is $42.50
To calculate the monthly payment for a health club membership with a payment plan, we first need to subtract the down payment of $50 from the total cost of $560. This leaves us with $510 to be paid in 12 equal monthly installments.
To find out how much each monthly payment would be, we divide the remaining balance ($510) by the number of months (12). Therefore, the monthly payment would be:
$510 ÷ 12 = $42.50
Therefore, A member would need to pay $50 down and $42.50 per month for the next 12 months to cover the cost of a $560 annual membership.
To learn more about payment click on,
https://brainly.com/question/24495205
#SPJ4
The heart rates (in beats per minute) of 41 randomly selected finishers of the Chicago Marathon, five minutes after they completed the race, had sample mean x = 132 and sample variance s2 = 105. Assuming that the heart rates of all finishers of the Chicago Marathon five minutes after completing the race are normally distributed, obtain a 95% confidence interval for their mean.
Answers
The 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute for variance.
To find the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race, we can use the following formula:
\(CI = x +- (t * (s / \sqrt{n} ))\)
where:
- CI is the confidence interval
- x is the sample mean (132)
- t is the t-value corresponding to the 95% confidence level
- s is the square root of the sample variance (the sample standard deviation)
- n is the sample size (41)
Step 1: Calculate the sample standard deviation
\(s = \sqrt{s^2} = \sqrt{105}\)≈ 10.25
Step 2: Find the t-value for a 95% confidence level with 40 degrees of freedom (n - 1)
Using a t-table or calculator, we find that the t-value is approximately 2.021.
Step 3: Calculate the margin of error
Margin of Error =\(t * (s / \sqrt{n} ) = 2.021 * (10.25 / \sqrt{4} )\) ≈ 3.26
Step 4: Calculate the confidence interval
CI = x ± Margin of Error = 132 ± 3.26
CI = (128.74, 135.26)
So, the 95% confidence interval for the mean heart rate of Chicago Marathon finishers five minutes after completing the race is (128.74, 135.26) beats per minute.
Point D is located at (-1, 6) on the coordinate plane. Point D is reflected over the
y-axis to create point D'. Point D'is then reflected over the r-axis to create point
D". What ordered pair describes the location of D"?
Answers
Answer:
(1, -6)
Step-by-step explanation:
After reflecting over y axis: (1, 6)
After reflecting (1, 6) over x axis: (1, -6)
I think you made a typo in your question. I think you meant "x-axis" instead of "r-axis"
explain the difference between a parameter and a statisitc, explain the difference between p and p hat, what is maent by sampling variabiloty
Answers
The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.
Parameter and statistic: Parameter is a value that describes the population, while statistic is a value that describes a sample.
Parameters are usually represented using Greek letters, while statistics are usually represented using Roman letters. In other words, a parameter is a population characteristic, whereas a statistic is a sample characteristic.
P and p hat: P represents the true proportion of a population with a particular attribute, while p hat represents the proportion of a sample with that attribute. P hat is an estimate of the true proportion p, which may differ from the actual proportion due to sampling error.
Sampling variability: Sampling variability is the variation in sample statistics that occurs from sample to sample. It is the result of the fact that different samples of the same size drawn from the same population will produce different estimates of the population parameter due to random sampling error. The sampling variability can be reduced by increasing the sample size. Hence, it is essential to ensure that a large enough sample size is used to obtain reliable estimates of population parameters.
To know more about Sampling variability: https://brainly.com/question/30530844
#SPJ11
a combination of values that, when arranged correctly, result in a final value.
Answers
Combinations and sequences are widely used in mathematics to explain and assess situations in which the order or selection of components might influence the final result.
What is combination?A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.
Here,
A combination is a grouping of things from a bigger set in which the order of the components is irrelevant. A sequence is a collection of elements that are ordered in a precise order. Combinations and sequences are frequently used in mathematics to describe and evaluate situations where the order or selection of components might impact the final outcome, such as in combinatorics, probability, and statistics.
To know more about combination,
https://brainly.com/question/20211959
#SPJ4
Complete question:
A combination of values that, when arranged correctly, result in a final value. true/false
Please helppppppppppppppppppppp
Answers
Answer:
No I won't.....
But OK let's help.... Will earn some good deeds
Isn't the ans 12??
Yes it's........... 12cm
si tardamos 20 minutos en recorrer una distancia a una velocidad de 40 km/h
1)cuanto tardaremos en recorrer dicha distancia si circulamos a 50 km/h
2) si la velocidad maxima en la zona es de 90 km/h a que porcentaje corresponden los 50 km/h?
porfa necesito el paso a paso :(
ya se q son inversas solo necesito el paso a paso
Answers
1) El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
¿Cómo analizar móviles a rapidez constante?
1) En este problema tenemos el caso de un vehículo que se desplaza a rapidez constante. Aquí tenemos que la rapidez (v), en kilómetros por hora, es inversamente proporcional al tiempo invertido (t), en minutos.
[(40 km /h) / (50 km / h)] = t / 20 min
4 / 5 = t / 20
t = 80 / 5
t = 14 min
El vehículo tardará 14 minutos en recorrer la misma distancia a una rapidez de 50 kilómetros por hora.
2) El porcentaje correspondiente a la rapidez reportada se calcula mediante porcentajes:
r = [(50 km / h) / (90 km / h)] × 100 %
r = 55.556 %
La rapidez registrada equivale al 55.556 % de la velocidad máxima de la zona.
Para aprender más sobre proporcionalidad inversa: https://brainly.com/question/25975416
#SPJ1
Explain how you know that segment DE is not parallel to segment BC.
Answers
Answer:
a person who fortells an event is called
Probability and Statistics - Colored Points Six points are drawn from uniform distribution U10,1]. The first three points are marked green and the next three are marked red on the real line. What is the probability that all adjacent points differ in color? Pick one of the choices 1/20 1/10 1/6 1/5 Clear selection Probability and Statistics - Dice Consider an unbiased six-faced dice with integers 1 through 6 marked on the faces. Assume the dice is thrown repeatedly, until the sum of the numbers cast till that point is a multiple of 6. What is the expected number of throws? Pick one of the choices 03 4.5 Clear selection
Answers
The probability that all adjacent points differ in colour is \(\frac{1}{5}\).
What is probability ?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Have given ,
We have first three colour Green that is g1 , g2 and g3
And We have next three colour red that is r1 , r2 and r3
The probability that all adjacent points differ in colour = 3! * \(^{4}C_{3}\) 3! / 6!
=> \(\frac{ 3! * 4! *3!}{6!}\)
=> \(\frac{1}{5}\)
The probability that all adjacent points differ in colour is \(\frac{1}{5}\).
To learn more about probability visit : brainly.com/question/30034780
#SPJ4
Mrs. Trotta drives 31 miles each day when she goes to work. How many miles does she drive in a 5 day work week?
Im a little lazy and i dont feel good so someone answer this please
Answers
Find the DISTANCE of line segment AB with point A
Answers
Answer:
34
Step-by-step explanation:
x-y
Help with slope pleaseee
^^
Answers
You have to do to get the answer
anyone knows this??
Answers
Answer:
the answer is B 40 because∆ABC is a triangle
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Describe a scenario that would result in an equation similar to the equations for Scenarios 1 and 2. Post your scenario and the corresponding equation to the discussions area.
Answers
Answer:
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)
considering theres no like first hour pay or something then it would be
Equation: m = 8h
Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.
Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost
Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.
Equation: c = 2h
Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)
Equation: t = 2m
A company makes two products, X1 and X2. They require at least 20 of each be produced. Which set of lower bound constraints reflect this requirement
Answers
To represent the requirement that a company makes at least 20 units of products X1 and X2, you can use the following set of lower bound constraints:
\(1. X1 \geq 20\\2. X2 \geq 20\)
These constraints indicate that the production of X1 must be greater than or equal to 20 units, and the production of X2 must also be greater than or equal to 20 units.
To know more about lower bound refer here
https://brainly.com/question/32210830#
#SPJ11
what's the answer thanks !!!! i need help asap
Answers
where is the question pleass?Then I can see if I cam help you.
Re-write the quadratic function below in Standard Form
y= 9(x - 1)(x + 7)
Answers
The value of quadratic function is,
⇒ y = 9x² + 54x - 63
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = 9 (x - 1) (x + 7)
Now, We can find the quadratic equation as;
⇒ y = 9 (x - 1) (x + 7)
⇒ y = 9 (x² + 7x - x - 7)
⇒ y = 9 (x² + 6x - 7)
⇒ y = 9x² + 54x - 63
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ1
John’s gross pay for the week is $500. He pays 1.45 percent in Medicare tax, 6.2 percent in Social Security tax, 2 percent in state tax, 20 percent in federal income tax, and $20 as an insurance deduction. He does not have any voluntary deductions. What is John’s net pay for the week?
A.
$331.75
B.
$333.75
C.
$332.75
D.
$330.75
E.
$335.75
Answers
John's net pay for the week is $341.00
To calculate John's net pay for the week, we need to subtract the various taxes and deductions from his gross pay.
Medicare tax: 1.45% of $500 = $7.25
Social Security tax: 6.2% of $500 = $31.00
State tax: 2% of $500 = $10.00
Federal income tax: 20% of ($500 - $7.25 - $31.00 - $10.00) = $90.75
Insurance deduction: $20.00
Now, let's calculate the total deductions:
Total deductions = $7.25 + $31.00 + $10.00 + $90.75 + $20.00 = $159.00
To find John's net pay, we subtract the total deductions from his gross pay:
Net pay = Gross pay - Total deductions
Net pay = $500 - $159.00
Net pay = $341.00
John's net pay for the week is $341.00.
None of the given answer options matches the calculated net pay.
For more such questions on net pay
https://brainly.com/question/14972403
#SPJ8
I need help.
someone help please!
Answers
Answer:
Step-by-step explanation:
The rule governing the number of magazines sold varies directly with the constant of proportion 10:
10 times the number of students comes out to 100: 10(10) = 100
25 times the number of students comes out to 250: 10(25) = 250
and so on.
In summary: the number of magazines sold is y = 10x, where x is the number of students involved.
henry scored 85, 76, 84, and 69 on four exams. what must he make on the fifth exam to have an average of 80?
Answers
Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.
What is the average?
This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.
Average = sum of all marks/total number of exams
80 =(85 + 76 + 84 + 69 + x)/5
80 = 314 + x/5
80 * 5 = 314 + x
400 = 314 + x
x = 400 - 314
x = 86
Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.
To learn more about average in mathematics, visit:
https://brainly.com/question/20118982
#SPJ4
Please help.
Algebra.
Answers
1. A
Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution.
--------------------------------------------------------------------------------------------------------------
2. C
That's right. If a system of equations has a solution, then their graphs intersect, and the point where they intersect is the solution because it's the point that satisfies each equation in the system.
Straight-line graphs with the same slope are parallel lines, and they never intersect, which is another way of saying they have no solution.