You have a bag full of 4 green marbles and 1 blue marble. You pick a marble out at random. If it's blue, you stopbecause you win 20 points. If not, you get another chance. Without replacing the green marble, you pick again. It'sblue, you win 10 points, otherwise you lose 20 points. Let X be the number of points you eam in this game. If you playedthis game 100 times, how many points can you expect to win (or lose)?
Answers
As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
\(\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}\)Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
\(\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}\)Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
\(\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}\)Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
\(P(x=10)=\frac{1}{4}\)Now,
Here, find the probability that no points for the first green ball is,
\(P(x=0)=\frac{4}{5}\)Now,
If you played this game 100 time, then the probability is,
\(\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}\)now,
For 100 times,
\(1.25\times100=125\text{ points.}\)Hence, 125 points can you expect to win.
Related Questions
Let the mean success rate of a Poisson process be 8 successes per hour.
a. Find the expected number of successes in a half-hour period.
b. Find the probability of at least two successes in a given half-hour period.
c. Find the expected number of successes in a two-hour period.
d. Find the probability of 10 successes in a given two-hour period.
Answers
The probability of 10 successes in a given two-hour period is 0.042 .Hence, the required values are:
a. Expected number of successes in a half-hour period = 4.
b.Probability of at least two successes in a given half-hour period = 0.9085
c. Expected number of successes in a two-hour period = 16.
d. Probability of 10 successes in a given two-hour period = 0.042
The mean success rate of a Poisson process is 8 successes per hour.
Now, we need to find:
a. Expected number of successes in a half-hour period.
b. Probability of at least two successes in a given half-hour period.
c. Expected number of successes in a two-hour period.
d. Probability of 10 successes in a given two-hour period.
a. Expected number of successes in a half-hour period:
Given that the mean success rate of a Poisson process is 8 successes per hour.
The number of successes in half an hour = λ * t = 8 * 0.5 = 4 successes
Therefore, the expected number of successes in a half-hour period is 4.
b. Probability of at least two successes in a given half-hour period:
To find the probability of at least two successes in a given half-hour period, we use the Poisson distribution formula:P (X ≥ 2) = 1 - P (X = 0) - P (X = 1)Where X is the number of successes in half-hour period and its distribution is given by Poisson with parameter λ = 4
The probability of zero successes, P (X = 0) = e-λλ⁰/ 0! = e-4 × 40! = 0.0183The probability of one success, P (X = 1) = e-λλ¹/ 1! = e-4 × 0.5/1 = 0.0732P (X ≥ 2) = 1 - 0.0183 - 0.0732 ≈ 0.9085
Therefore, the probability of at least two successes in a given half-hour period is 0.9085 (approximately).
c.Expected number of successes in a two-hour period :
The number of successes in a two-hour period = λ * t = 8 * 2 = 16 successes
Therefore, the expected number of successes in a two-hour period is 16.
d. Probability of 10 successes in a given two-hour period:
The parameter λ for a two-hour period = 16Let X be the number of successes in a two-hour period, then X is Poisson distributed with parameter λ = 16.The probability of 10 successes in a given two-hour period isP(X = 10) = e-16 × 1610! ≈ 0.042
Therefore, the probability of 10 successes in a given two-hour period is 0.042 (approximately). Hence, the required values are:
a. Expected number of successes in a half-hour period = 4.
b.Probability of at least two successes in a given half-hour period = 0.9085
c. Expected number of successes in a two-hour period = 16.
d. Probability of 10 successes in a given two-hour period = 0.042
For more questions on Probability .
https://brainly.com/question/30390037
#SPJ8
The expected number of successes in a half-hour period is 4. The probability of at least two successes in a given half-hour period can be calculated using the Poisson probability formula. The expected number of successes in a two-hour period is 16. The probability of 10 successes in a given two-hour period can be calculated using the Poisson probability formula.
Explanation:a. To find the expected number of successes in a half-hour period, we can use the formula E(X) = λt, where λ is the mean success rate and t is the time period. In this case, λ = 8 successes per hour and t = 0.5 hours. Therefore, E(X) = 8 * 0.5 = 4.
b. To find the probability of at least two successes in a given half-hour period, we can use the formula P(X ≥ k) = 1 - P(X < k), where k is the minimum number of successes. In this case, k = 2. The probability of getting less than 2 successes in a half-hour period can be calculated using the Poisson probability formula. Using this formula, P(X < 2) = e^(-λ) * (λ^0/0!) + e^(-λ) * (λ^1/1!). Finally, P(X ≥ 2) = 1 - P(X < 2).
c. To find the expected number of successes in a two-hour period, we can use the same formula as in part a. Here, we have λ = 8 successes per hour and t = 2 hours. Therefore, E(X) = 8 * 2 = 16.
d. To find the probability of 10 successes in a given two-hour period, we can again use the Poisson probability formula. Using this formula, P(X = 10) = e^(-λ) * (λ^10/10!).
Learn more about Calculating probabilities in a Poisson process here:https://brainly.com/question/32617473
#SPJ11
x+y-z= 6
3x - 2y + z = -5
x + 3y - 2z = 14
Answers
Answer:
( x , y , z) = ( 1 , 3 , - 2)
the solution
You would like to build a relative frequency distribution for this data set to easily compare it to another class of students.
What is the relative fequency for the third class, 160 - 169?
Enter answer as a percent (but do not include the percent symbol).
relative frequency = %
Answers
The relative frequency for the third class, 60 - 69 is equal to 12%.
What is a class width?In a frequency distribution table, a class width can be defined as the difference between the upper (maximum) and lower (minimum) boundaries of any class in a data set. This ultimately implies that, all classes must all have the same width in a frequency distribution table.
What is a frequency table?A frequency table can be used to graphically represent the frequencies or relative frequencies that are associated with a categorical variable.
How to calculate the relative frequency for the third class, 60 - 69?First of all, we would determine the total number of frequency as follows:
Total frequency = 12 + 11 + 6 + 10 + 11
Total frequency = 50.
Mathematically, relative frequency can be calculated by using this formula:
Relative frequency = class frequency/total frequency × 100
Relative frequency = 6/50 × 100
Relative frequency = 0.12 × 100
Relative frequency = 12%.
Read more on frequency table here: brainly.com/question/20744563
#SPJ1
Complete Question:
You would like to build a relative frequency distribution for this data set to easily compare it to another class of students.
What is the relative frequency for the third class, 60 - 69?
What is the reciprocal of 5 6/7 ?
Answers
The pressure, P (in lbs/ft2 ), in a pipe varies over time. Five times an hour, the pressure oscillates from a low of 90 to a high of 230 and then back to a low 90. The pressure at t = 0 is 90.
Question: Find a possible formula for P=f(t)
Answers
P=160-70*cos(2π*(1/12)*t)
• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).
First, we find the amplitude by taking the difference between the peak values and dividing by two:
Amplitude=(230+90)/2=70
We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:
90+70=160
230-70=160
This tells us that the Center Value=160
The frequency that we are operating at is given as:
f = 5/hour
so in minutes
f=5*(1/60)/minute=5/60=1/12 per minute
So, combining everything we get
P=160-70*cos(2π*(1/12)*t)
Learn more about Pressure here
https://brainly.com/question/26040104
#SPJ9
Please help !!!!!! 20 points
Answers
The value of x in the polygon will be 13.25 degrees.
The value of x is 10.
We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.
How to calculate the valueThe sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.
Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees
Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:
Measure of one angle = 3960/24 = 165 degrees
165 = 12x + 6
159 = 12x
x = 13.25
Therefore, the value of x is 13.25 degrees.
Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.
Therefore, we have:
731x+86° = 7380°
Solving for x, we get:
731x = 7294°
x = 10
Therefore, the value of x is 10.
The equation that can be used to find the value of x is:
(9x+48)° + (15x-24)° = (n-2)*180°
24x + 24 = (n-2)*180°
Dividing both sides by 24, we get:
x + 1 = (n-2)*15°
Subtracting 1 from both sides, we get:
x = (n-2)*15° - 1
Learn more about polygon on
https://brainly.com/question/1592456
#SPJ1
7, 11, 2, 18, -7, __ find the missing pattern.
Answers
Answer:
-11
Step-by-step explanation:
the candle was 1 inches long when new.Each half hour 3/4 inch of the candle burned away.After 4 hours,how long was the candle
Answers
After 2 hours, the candle would have burned away another 1.5 inches (4 half-hour periods * 3/4 inch burned in each period), leaving it with a length of 0 inches. At this point, the candle has completely burned down.
Therefore, after 4 hours, the length of the candle would be 0 inches.
What is the formula for theses graph
Answers
Maria has 56 flower seeds. She wants to put an equal amount of seeds into 8 bags How many seeds will go in each bag?
Answers
Answer:
7 seeds will go into each bag
Given:
56 flower seeds need to be put into 8 separate bags.
To find out how much go into each bag you will divide the number of seeds by the number of bags
56/8=7
So 7 seeds will go into each of the 8 bags
500 ML = __ L
Perform numerical calculations
Answers
Answer:
500*10^6 L or 5.00*10^8 L.
Step-by-step explanation:
Capital M shows mega which equal to 10^6.
So, 500 ML = 500*10^6 L
or 5.00*10^8 L.
Answer:
0.5
Step-by-step explanation:
Step 1:
1 L = 1000 ML
Step 2:
500 ML ÷ 1000
Answer:
0.5 L
Hope This Helps :)
A variable needs to be eliminated to solve the system of equations below. Choose the
correct first step.
8x + 9y = -82
Sy = 89
--
A.Subtract to eliminate x.
B.Add to eliminate y.
C.Subtract to eliminate y.
D.Add to eliminate x.
* someone please answer this *
Answers
Answer:
Add to eliminate Y!
Step-by-step explanation:
each side is a -2y, you do the opposite- which is addition :D
Hope this helped you! Have a nice day!
-7x-3=12 what is the answer to this question??.
Answers
Add 3 to the other side
-7x = 15
Divide both sides by -7
x = 15/ -7
Plz help me solve this algebra problem
Answers
Answer:
Exact Form:
x = 2 √ 2 − 1 3 , − 2 √ 2 − 1 3
Decimal Form:
x = 2.49509379 , − 3.16176045
Step-by-step explanation:
Simplify the decimals as needed
Which statement is true?
- A checking is account is where you want to keep all of your money for spending and saving,
-A checking account is where you want to keep your spending money and a savings account is
where you want to keep your savings
-A checking account is where you want to keep your savings and a savings account is where you
want to keep your spending money,
A savings account is where you want to keep all of your money for spending and saving.
Answers
Answer:
B
Step-by-step explanation: The checking account is the account that you write checks out of, and the savings account is self explanatory, you put your savings there
Answer: B
Step-by-step explanation:
Checking accounts are used for spending. Savings limit your withdraws and give you some money back in a small % interest, typically at the end of a year term.
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer: 89y
89y
Step-by-step explanation: 89y
89y
Which transformations could have occurred to map AABC
to AA"B"C"?
O a rotation and a dilation
O a rotation and a reflection
O a reflection and a dilation
O a translation and a dilation
Answers
Answer:
A reflection and a dialation
Step-by-step explanation:
Reflection is when you flip a figure over a line. Rotation is when you rotate a figure a certain degree around a point. Dilation is when you enlarge or reduce a figure.In this case a rotation is not nessasary, so I would suggest a reflection in the y-axis and a dialation to shrink the triangle to A'B'C'
So for the transformations that could have occurred to map ABC to A'B'C' you should choose the answer
a reflection and a dialation
The transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Key Facts on TransformationsReflection is simply flipping a shape over an axis.Dilation means enlarging a figure or reducing the size of a figure.Rotation simply involves rotating a figure around a given point while maintaining same size.Translation is shifting the points of a figure to move it to another position.Thus, in the transformation shown, figure ABC was reflected over the y-axis and then dilated to give A'B'C'.
Therefore, the transformations that occurred to map ABC to A'B'C are: C. a reflection and a dilation
Learn more about transformation on:
https://brainly.com/question/1462871
If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
Answers
I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
\(f(x)\ge2\)Bad study time as:
\(f(x)<2\)The last one can represent the study habits of Grade 7 students.
3. [-/2 Points]
Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.)
4x² + 5x-6
x+2
DETAILS
20
lim
X--2
Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result.
g(x)
LARCALC12 1.3.044.
Need Help? Read It
Answers
The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2
To find the limit as x approaches -2, we substitute -2 into the function:
f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
= 4(4) - 10 + 12 + 2
= 16 - 10 + 12 + 2
= 20
Therefore, the limit of the function as x approaches -2 is 20.
To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.
However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.
For more question on function
https://brainly.com/question/11624077
#SPJ8
3. Mateus recebe a visita do seu avô Pedro a cada 15 dias. João, o tio dele, o visita a cada 100
e, devido a escalas de trabalho, a cada 12 dias Mateus vai à praia com seus pais. Um belo dia Mans
recebeu a visita do seu avô, do seu tio e foi à praia com seus pais (com o avô e o tio que o visitavam nese
dia). Quantos dias depois este acontecimento se repetirà?
Answers
Answer:
Este acontecimento se repetirá 300 dias depois.
Step-by-step explanation:
Quando os eventos se repetirão no mesmo dia?
Cada evento tem uma frequência.
Eles ocorrem simultaneamente a cada x dias, e x é dado pelo MMC(Mínimo Múltiplico Comum) entre as frequência.
Neste problema:
A cada 15 dias o avô visita.
A cada 100 dias o tio visita.
A cada 12 dias vai à praia.
Quantos dias depois este acontecimento se repetirá?
Os três no mesmo dia vão se repetir após x dias, em que x é dado pelo MMC de 15, 100 e 12
MMC de 15, 100 e 12
Fatorando simultâneamente estes valores:
15 - 100 - 12|2
15 - 50 - 6|2
15 - 25 - 3|3
5 - 25 - 1|5
1 - 5 - 1|5
1 - 1 - 1
Então:
mmc(15,100,12) = 2*2*3*5*5 = 300
Este acontecimento se repetirá 300 dias depois.
i need help. this is algebra 2 and im currently going “bootcamp for it*
Answers
Answers:
8
6
1
3
Reason:
Add 5 to each value in the f(x) column.
Example: 3+5 = 8 for the first row.
This will shift each point 5 units up. This is because we're moving 5 units up the y axis.
How many solutions does this system of equations have y = -1/3x + 7. y = -2x^3 + 5x^2 + x - 2
Answers
The system of equations has one solution.
How many solutions does this system has?To check this, we can graph the two equations of the system:
y = (-1/3)x + 7
y = -2x³ + 5x² + x - 2
On the same coordinate axis, and check how many times do the graphs intercept.
The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.
Learn more about systems of equations at:
https://brainly.com/question/13729904
#SPJ1
Sales of different ice cream flavors at a small ice cream shop were recorded for one week. The graph shown here displays the sales of each different flavor.
What is the mean of the data?
A)6
B)7
C)8
D)9
Answers
Answer:
its c
Step-by-step explanation:
i did da quiz
Mean of Number of scope is 8
Given that;
Number of scope of Vanilla = .6
Number of scope of chocolate = 14
Number of scope of strawberry = 10
Number of scope of Butter pecan = 6
Number of scope of cookie dough = 4
Number of scope of moose track = 8
Find:
Mean of Number of scope
Computation:
Mean of Number of scope = [6+14+10+6+4+8] / 6
Mean of Number of scope = [48] / 6
Mean of Number of scope = 8
Learn more:
https://brainly.com/question/19715580?referrer=searchResults
Find the value of x in the parallelogram
Answers
The value of x in the parallelogram is 112°.
In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.
To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.
Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.
Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.
Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.
This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.
For the given question, we know x° + 68° = 180°.
Then x° = 180° - 68°
x° = 112°
For more such questions on parallelogram
https://brainly.com/question/20526916
#SPJ8
Jake is 5 years older than his brother Kevin.
Kevin is k years old. Write an algebraic
expression for Jake's age.
Answers
Answer:
5+k
Step-by-step explanation:
its saying jake is 5 MORE then kevin so either add or multiply.
Four less than the product of three and a number
Answers
four less than three times that number is:3x-4
is:=
three more than two times the number: 2x+3
Problem to solve:
3x-4=2x+3
3x-2x-4=2x-2x+3
x-4=3
x-4+4=3+4
x=7
Calculated:
3(7)-4=2(7)+3
21-4=14+3
17=17
Dan gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many marshmallows as smarties. What proportion of the bag of sweets are smarties?
Give your answer in its simplest form
Answers
The proportion of the bag of sweets are smarties is 1/6.
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Now it is given that,
There are 3 types of sweets in the bag.
Let s be number of the smarties sweet that Dan picks
c be the number of cola bottles that Dan picks
and m be the number of marshmallows sweet that Dan picks
Now since, He picks 3 times as many cola bottles as smarties
Thus,
c = 3s
And, He picks twice as many marshmallows as smarties.
m = 2s
Now the total sweets in the bag = c + s + m
Substituting the value of c and s in the total sweets we get,
3s + s + 2s = 6s
Now, To find out the proportion of the bag of sweets that are smarties, divide the number of smarties by the total of sweets
Thus, the proportion of the bag of sweets are smarties = s/6s = 1/6
this is the required proportion of smarties in the bag.
Thus, the proportion of the bag of sweets are smarties is 1/6.
To learn more about proportions :
brainly.com/question/8099778
#SPJ1
Can you please help me
Answers
Answer:
3. D
4. I
5. E
6. G
7. J
8. B
9. A
10. H
Using 50 random numbers given below, compute the mean and standard deviation. 0.937776 0.270012 0.243785 0.590701 0.824982 0.131805 0.879337 0.741998 0.254683 0.080259 0.419321 0.928220 0.958430 0.980182 0.263900 0.063119 0.762096 0.485612 0.662900 0.362242 0.724796 0.307736 0.305021 0.417052 0.054337 0.323357 0.069662 0.843387 0.353107 0.074262 0.735596 0.175095 0.390508 0.668932 0.029861 0.205228 0.387740 0.962169 0.646565 0.423914 0.754782 0.156719 0.773113 0.546335 0.323573 0.649740 0.214082 0.382383 0.383982 0.030539 Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
Answers
The mean is 0.477514 (rounded to 6 decimal places).
The standard deviation is 0.288919 (rounded to 6 decimal places).
How to Solve the Problem?To calculate the mean and standard deviation, we will use the following formulas:
Mean = (sum of all values) / (number of values)
Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]
Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:
Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514
Therefore, the mean is 0.477514 (rounded to 6 decimal places).
Now we will calculate the standard deviation:
Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919
Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).
Learn more about mean here: https://brainly.com/question/20118982
#SPJ1
Find the slope intercept equation of the line.
