Given information, we are required to find the Joint Probability Mass Function of (X, Y), where X and Y are the smaller and larger number of points, respectively, when two dice are rolled.
The sample space of rolling two dice is {1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6}, {3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6}, {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6}, {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6}, {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}. Let A = {1, 2, 3, 4, 5, 6} be the sample space of a dice, which means the probability of each outcome is 1/6.
Now, we need to calculate the probability of rolling i and j, where X is the smaller number, and Y is the larger one. Therefore, P (X = i, Y = j) = P (i, j) - P (i, i) - P (j, j) if i≠j, where P (i, j) represents the probability of rolling i and j.
However, if i = j, then P (X = i, Y = i) = P (i, i). For i=1,2,3,4,5,6, P (X = i, Y = i) = 1/6.
We can also write P (X = i, Y = i) = P (X = i)P (Y = i). Therefore, P (X=i, Y=j)=P(i,j)−P(i,i)−P(j,j)={1/36 if i≠j}{1/18 if i=j}.
(b) X and Y are not independent since knowing X affects Y. If X is known to be 2, then Y can only be in the range of 3 to 6. Therefore, P(Y=5|X=2) ≠ P(Y=5). This shows that X and Y are not independent.
(c) Let p(i) represent the probability mass function of X, which is the probability of the smaller number being i. For i = 1, 2, 3, 4, 5, 6, P(X=i)=P(X=i,Y>i)+P(X=i,Y=i)={5/36 if i=1}{4/36 if i=2}{3/36 if i=3}{2/36 if i=4}{1/36 if i=5}{0 if i=6}
(d) The required probability of P(Y=5|X=2) = P(X=2,Y=5)/P(X=2). The probability of X=2 is P(X=2) = 4/36 = 1/9. Since X=2, the favorable outcome is {(2, 5)}, therefore, P(X=2,Y=5) = 1/36. The required probability is P(Y=5|X=2) = P(X=2,Y=5)/P(X=2) = (1/36)/(1/9) = 1/4 = 0.25. Hence, the probability that Y=5 when X=2 is 0.25.
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In the diagram shown, what is the ratio of shaded parts to unshaded parts?
6 unshaded squares and 9 shaded squares.
For every 2 shaded parts there are 3 unshaded parts.
For every 9 shaded parts there are 2 unshaded parts.
For every 3 shaded parts there are 6 unshaded parts.
For every 3 shaded parts there are 2 unshaded parts.
Answer:
For every 3 shaded parts there are 2 unshaded parts
Step-by-step explanation:
because there are 3 blue shaded and 2 white that have not been shaded
Answer:
6,9 3,3 9,2 3,6 3,2
this is the ratios
7. If x = 14, which equation is true?
I need help pls
Plz help
a) The answer is 3/3, as that makes it a whole. Whole = 1.
b) The answer is 8 as having a denominator of 1 makes it a whole already. That's 8 wholes.
Answer:
(a)= 3
(b)=8
Step-by-step explanation:
3/3 = a whole number which i 1
8/1=any number with a 1 underneath is just a whole number as a fraction
you can also divide:
3 divided by 3 is 1
8 divided by 1 is 8
The following scores represent students' test grades in Ms. Mihal's math class.
Test Scores
78 84 78
85 93 85
84 78
93 85
84 78 84 78
93 85 93 85
What is the median score for Ms. Mihal's math class?
A
93
B
84.5
C
85
D
84
F
I don't know yet
Answer:
Definitely B 84.5
Just worked it out
Answer:
84.5
Step-by-step explanation:
List the numbers in order. I cross them out smallest then biggest and so on until I get either the one in the middle or the two in the middle. If It's only one in the middle that's your answer. If it's two in the middle find the average. In this case the middle two numbers were 85 and 84. 85+84= 169. 169/2=84.5. Hope this helps :)
The Bike Rental Shop charges $12
plus $9 an hour for renting a bike.
Darnell paid $57 to rent a bike. How
many hours did he pay to have the
bike checked out?
Answer:
5 hours
Step-by-step explanation:
Let x represent the number of hours
12 + 9x = 57
9x = 57 - 12
9x = 45
x = 5
10 is subtracted from 2 times a number
Answer: the equation is 2n-10
Negative numbers are always shown with a _________________________ sign.
Answer:
Minus -
Step-by-step explanation:
12:35 on Sunday.
I am back with a handful of geometry questions. I would like you to answer this question and explain or show all of your work.
I will mark Brainlest for an accurate answer!
If the image is to blurry try clicking on it. If it is still to blurry, let me know in the comments. If you have any other questions about the problem, let me know.
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Answer:
see attached
Step-by-step explanation:
Triangle ABC reflected over line l into triangle A'B'C'
Answer:
see attached
Step-by-step explanation:
to reflect the image along y-axis as required. or mirror line
ABC --->> A'B'C'
jenny ran the 100 yards dash in 25 seconds how many feet could jenny run each second? explain your work (1 yard=3 feet)
How much greater is the area of a circle with a radius of 7.6 inches than the area of a square with a side length of 5 inches?
Answer:
2.6
Step-by-step explanation:
i think thats the answer cuh
8 ( 11 - 2b ) = -4 ( 4b - 22 )
Tina buys Space Warriors II for $11.26, including tax. She pays with a $20 bill. How much change should she receive?
Answer:
$8.74
Step-by-step explanation:
If tina paid with a $20 bill and the cost of the game was $11.26 than we would subtract 11.26 from 20 to get the answer of $8.74 money she gets back
Owen is signing up for a gym membership with a one time fee to join and then a monthly fee to remain a member. The one time fee to join the gym is $100 and the total cost of the membership, including the joining fee, would be $200 for 2 months. Write the equation for C, in terms of t, representing the total cost of the gym membership over t months
Answer:
Use mathpapa it helps a lot
Step-by-step explanation:
Mathpapa.com
The equation for the total cost of the gym membership over t months is
C = 100 + 50t.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
One time fee = $100
The total cost of the membership after 2 months.
= $200
This means,
The cost per month.
= (200 - 100) ÷ 2
= 100 ÷ 2
= 100/2
= $50
The cost of the gym membership over t months.
= 100 + 50t
Thus,
The equation is C = 100 + 50t.
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What is the gradient of the graph shown?
Step-by-step explanation:
i hope i have been useful buddy.
good luck ♥️♥️♥️♥️.
PLZZZ HELP IN DIRE NEED FOR ASSISTANCE PLZZ
Select the correct answer.
Which point satisfies the system of equations y = 3x − 2 and y = -2x + 3?
A.
B.
C.
D.
given the equation 2x+y=12. a) what is the value of x, when the value of y is 4
Martin is building a model .he cuts two pieces of wood taht are each 6, 1/3 inches long from a board with a total length of 18 inches .what is the length, in inches, od the remaining part of the boards
Answer:
5 1/3
Step-by-step explanation:
6 1/3 + 6 1/3 = 12 2/3 + 5 1/3 = 18
The remaining part of the wood is 5(1/3) out of a total length of 18 inches.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Martin is building a model he cuts two pieces of wood that are each 6, 1/3 inches long from a board with a total length of 18 inches.
The remaining part will be calculated as below:-
Length of the two parts = 6(1/3) + 6(1/3)
= 12(1/3)
The remaining part will be calculated as,
R = 18 - 12(1/3)
= 5(1/3)
Therefore, the remaining part of the wood is 5(1/3) out of a total length of 18 inches.
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If the interest rate on a nominal bond is 9% today for three years when expected inflation is 2% on average, what is the real interest rate paid at the end of the three years if actuall inflation was
The real interest rate paid at the end of three years can be calculated by subtracting the average inflation rate from the nominal interest rate. In this case, with a nominal interest rate of 9% and an average expected inflation rate of 2%, the real interest rate would be 7%.
The real interest rate is the nominal interest rate adjusted for inflation, representing the true return on an investment. To calculate the real interest rate, we subtract the average inflation rate from the nominal interest rate. In this scenario, the nominal interest rate is 9% and the average expected inflation rate is 2%.
By subtracting 2% from 9%, we find that the real interest rate paid at the end of the three years is 7%. This means that after accounting for inflation, the investor can expect a real return of 7% on their investment over the three-year period.
Considering inflation is essential because it erodes the purchasing power of money over time. By accounting for inflation, the real interest rate provides a more accurate measure of the return on investment. In this case, the real interest rate of 7% indicates that the investor is effectively earning a 7% return above and beyond the rate of inflation, providing a positive real return.
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MULTIPLE CHOICE ASAP
Consider the following statement: If 4x = 8, then x = 2.
What is the inverse of the statement?
more than one can be selected
If x = 2, then 4x = 8.
If x ≠ 2, then 4x ≠ 8.
If 4x ≠ 8, then x ≠ 2.
If 4x = 8, then x = 2.
Answer:
If x = 2, then 4x = 8.
Step-by-step explanation:
If x = 2, then 4x = 8.
Answer:
i think it is the third option
Step-by-step explanation:
inverse= -p ---> -q
Can somone help me do this it's because I don't understand it :)
Answer:
(1.2x - 2)(x - 5) < 2x(.6x + 1)
1.2x² - 8x + 10 < 1.2x² + 2x
10 < 10x
x > 1
Solve 3v -12 = 15
v = -9
v = 9
v = 1
v = -1
Answer:
v=9
Step-by-step explanation:
Answer:
v
Step-by-step explanation:
A wall is covered with 6 wood panels. Each panel is a square with a side length of "X"
feet. Write an expression to represent the total area, in square feet, covered by the
wood panels. Do not include spaces in your answer.
The expression to represent the total area, in square feet, covered by the
wood panels is to be considered as the [tex]6x^2[/tex].
Calculation of an expression:Since
A wall is covered with 6 wood panels. Each panel is a square with a side length of "X" feet.
So based on this, we can say that The expression to represent the total area, in square feet, covered by the wood panels is to be considered as the [tex]6x^2[/tex].
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An angle that has a measure greater than 0⁰ and less than 90⁰
Answer:
Obtuse
Step-by-step explanation:
The obtuse has a over 90 ° angle and is greater than that
Answer:
Acute angle
Step-by-step explanation:
An angle that has a measure greater than 0⁰ and less than 90 is known as acute angle
0.4(12-2)=22.2-(6x+7)
Answer:
x=1.866667
Step-by-step explanation:
The equation for Constant of Proportionality is y = kx? If you solved for the letter k instead of y, would the correct equation. be y/x = k? YES or NO
which of these is a factor in this expression?
7z^4-5+10(y^3+2)
The expression [tex]7z^4 - 5 + 10(y^3 + 2),[/tex] the factor is "10" since it multiplies the expression [tex](y^3 + 2)[/tex] to contribute to the overall product.
In the expression [tex]7z^4 - 5 + 10(y^3 + 2),[/tex] the term "10" is a factor.
To understand factors in this context, let's define them.
In algebra, factors are expressions or numbers that are multiplied together to obtain a product.
In the given expression, we have three terms: [tex]7z^4, -5,[/tex] and [tex]10(y^3 + 2).[/tex]
The term "10" is a factor because it is multiplied by the expression [tex](y^3 + 2).[/tex]
When we distribute 10 to the expression inside the parentheses, we get 10y^3 + 20.
Thus, "10" serves as a factor in the overall expression.
However, it's important to note that the term "-5" is not considered a factor because it is not being multiplied by any other expression or number.
It is a standalone constant term.
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Please make it a fraction and simplify it!
Answer: 4 and 4/5
Step-by-step explanation:
Can someone plz help me???Answer and explaination I’ll give brainlist and points
Answer:
X = 12
Step-by-step explanation:
Basically, just start with 11 and do all of the steps backwards, so multiply 11 by 5, which is 55, then add 2, 57. divide by 3, which is 19, then subtract 7, and you'll get the original number, 12.
Answer:
x = 12
Step-by-step explanation:
Following the steps in the flowchart
(1) Input the number x
x
(2) Add 7
x + 7
(3) Multiply by 3
3(x + 7)
= 3x + 21
(4) Subtract 2
3x + 21 - 2
= 3x + 19
(5) Divide by 5
[tex]\frac{3x+19}{5}[/tex]
(6) Output the number 11
[tex]\frac{3x+19}{5}[/tex] = 11 ( multiply both sides by 5 )
3x + 19 = 55 ( subtract 19 from both sides )
3x = 36 ( divide both sides by 3 )
x = 12
Estimate by rounding the second factor to the nearest ten. Then enter the product.
9x 93
The estimate is
The product is
(NEED DONE QUICK) Triangle ABC has a midsegment at DF and segment DF is parallel to segment BC.
What is the value of x?
Answer:
x = 25Step-by-step explanation:
Midsegment equals to half of the base
BC = 1/2 DF3x + 1 = 1/2*8(x - 6)3x + 1 = 4x - 244x - 3x = 1 + 24x = 25Answer:
x=25
Step-by-step explanation:
