The minimum sample size required is 108.
What is the standard deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. A low standard deviation means data are clustered around the mean, and a high standard deviation indicates data are more spread out.
To find the minimum sample size required, we can use the formula for the margin of error for a confidence interval for a mean:
margin of error = (z*s) / (√n)
where z is the z-score corresponding to the desired confidence level (in this case, z = 1.28 for an 80% confidence interval), s is the standard deviation of the population, and n is the sample size.
We are given that the margin of error should be no more than 0.06 and that the standard deviation is 0.9. We can solve for n by rearranging the formula and substituting in the given values:
n = [(zs) / margin of error]²
= [(1.280.9) / 0.06]²
= approximately 107.5
Since the sample size must be an integer, we must round up to the next integer, which is 108.
Hence, the minimum sample size required is 108.
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A trail mix recipe calls for 3 cups of raisins and 4 cups of peanuts. Mitt made trail mix for a party and used 5 cups of raisins and 6 cups of peanuts. Did he use the correct ratio of raisins to peanuts?
Answer: no
Step-by-step explanation:
Recipe calls for a 3:4 ratio of raisins to peanuts
If his intention was to make a 1.5x recipe, he should have used 6 cups peanuts and 4-1/2 cups raisins (not 5!) to make the recipe in the correct ratio.
Answer Questions 9 to 11 using the lines shown in the coordinate grid below.
Question# 5, Is it true that m is parallel to n? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and angels and calculations for all questions.
Question# 6, Is it true that m is congruent to p?
Question#7 Is it true that n congruent to p?
Answer:
Step-by-step explanation:
Find the equation of lines m, n and p
The equation of line:
[tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]
Line m: (-3,2) (3,6)
x₁=-3 x₂=3 y₁=2 y₂=6
[tex]\displaystyle\\\frac{x-(-3)}{3-(-3)} =\frac{y-2}{6-2} \\\\\frac{x+3}{3+3} =\frac{y-2}{4} \\\\\frac{x+3}{6}=\frac{y-2}{4}[/tex]
Multiply both parts of the equation by 4:
[tex]\displaystyle\\\frac{x+3}{6}(4)=y-2\\\\\frac{2}{3} (x+3)=y-2\\\\\frac{2}{3}x+2=y-2\\\\\frac{2}{3}x+2+2=y-2+2\\\\\frac{2}{3}x+4=y\\\\Thus,\ y=\frac{2}{3} x+4\\\\Hence,\ m_m=\frac{2}{3}[/tex]
Line n: (-5,-5) (5,1)
x₁=-5 x₂=5 y₁=-5 y₂=1
[tex]\displaystyle\\\frac{x-(-5)}{5-(-5)}=\frac{y-(-5)}{1-(-5)} \\\\\frac{x+5}{5+5}=\frac{y+5}{1+5} \\\\\frac{x+6}{10}=\frac{y+5}{6}[/tex]
Multiply both parts of the equation by 6:
[tex]\displaystyle\\\frac{3}{5}( x+5)=y+5\\\\\frac{3}{5} x+3 =y+5\\\\\frac{3}{5} x+3-5=y+5-5\\\\\frac{3}{5} x-2=y\\\\Thus,\ y=\frac{3}{5}x-2\\\\Hence,\ m_n=\frac{3}{5}[/tex]
Line p: (3,-4) (-3,6)
x₁=3 x₂=-3 y₁=-4 y₂=6
[tex]\displaystyle\\\frac{x-3}{-3-3} =\frac{y-6}{6-(-4)} \\\\\frac{x-3}{-6} =\frac{y-6}{6+4} \\\\\frac{x-3}{-6}=\frac{y-6}{10} \\[/tex]
Multiply both parts of the equation by 10:
[tex]\displaystyle\\-\frac{5}{3} x+5=y-6\\\\-\frac{5}{3} x+5+6=y-6+6\\\\-\frac{5}{3} x+11=y\\Thus,\ y=-\frac{5}{3}x+11 \\\\Hence,\ m_p=-\frac{5}{3}[/tex]
[tex]Question# 5: \ m_m\neq m_n\ \ \ \ m\ isn't\ parallel \ to\ n\\\\Question# 6:\ m\ isn't \ congruent \ to\ p\\\\Question#7 :\ n\ isn't \ congruent \ to\ p[/tex]
[tex]n \bot p[/tex]
Answer:
5) No the lines are not parallel because in order for this to be true, the slopes have to be equal. Line m has a slope of 2/3 and line n has a slope of 3/5. Both slopes are not equal so it is not parallel
6) No, m is not congruent to p
7) No, n is not congruent to p
(Is there any chance that you meant to say perpendicular instead of "congruent"?)
Step-by-step explanation:
For two lines to be parallel the slopes have to be equal
See attached to see the rise over run
line m: 2/3
line n: 3/5
The slopes are not equal so the lines are not parallel.
A store owner decides to mark up all items by 30%. What is the selling price of an item that originally cost $30?
After the markup, the selling price of the item will be $39.
What is the selling price of an item that originally cost $30?
We know that a store owner decides to mark up all items by 30%, so basically we need to increase all the costs by 30%.
If the original cost is C, then the cost after the mark up will be:
P = C*(1 + 30%/100%)
P = C*(1 + 0.3)
P = C*(1.3)
In this case, we want to find the selling price P for an object whose original cost C is $30, then we can replace C in the equation above so we get:
P = $30*1.3 = $39
The selling price P is $39.
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Function 2
y=x+4
Rate of Change: 3/4 Rate of Change:
Which has the greatest rate of change?
Answer:
function 2
Step-by-step explanation:
function 1 has a slope of 8/7 which is equal to 0.75 and function 2 has a slope of 1 so function 2 is greater than function 1.
Answer: <
Step-by-step explanation:
One number is less than another number if their difference is less than zero.
Since x=2y-4 - 0.75 = -0.75 which is less than zero, x=2y-4 is less than 0.75
Therefore, x=2y-4 is 0.75 less/lower than 0.75
Determine the equation for the line. Write the equation in standard form through
the points
(3,-4) and (6,-2)
The standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4.
What is the equation of the line passing through the two-point?
To find the equation for the line through two points we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the points, and m is the slope of the line. The slope of the line is equal to the change in y over the change in x, which can be calculated as:
m = (y2 - y1) / (x2 - x1)
where (x2, y2) is the other point.
Substituting the given points and the formula for the slope into the formula for the equation of the line, we get:
y - (-4) = ((-2) - (-4)) / (6 - 3) (x - 3)
This simplifies to:
y + 4 = -2/3 (x - 3)
To write the equation in standard form, we can distribute the -2/3 and then rearrange the terms:
-2/3 x + y = 4
Hence, the standard form equation for the line through the points (3,-4) and (6,-2) is -2/3 x + y = 4
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Mrs. James is on a train traveling 42 m.p.h. As Mrs. James is looking out the window, a freight train traveling at 18 m.p.h. moving in the opposite direction meets and passes her. She noticed it took 8 seconds for the freight train to pass her. The freight train is ___ feet long.
The freight train is 88.88 feet long.
What is Speed- Distance Formula?Speed = Distance/Time
Distance = Speed X Time
Time = Distance / Speed
As the trains travel in opposite direction then
Relative speed = (42 + 18) = 60 Km/ hr
= 60 x 5/18 = 300/ 18
= 100/9 m/s
So, length of the freight train = 100/9 x 8
= 88.88 feet
Hence, The freight train is 88.88 feet long.
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Triangle ABC is similar to triangle A’B’C’. Find the value of x.
Answer:
x = 64
Step-by-step explanation:
63. 28
---- = ----
144. x
Now cross multiply:
144(28) = 63(x)
4,032 = 63x
x = 64
May I have a brainliest? Thank you!
6x – 16 = 20 pls i need help i dont understand
Answer:
x=6
Step-by-step explanation:
6x-16=20
Add 16 to both sides
6x-16=20
+16. +16
6x=36
Divide 6 to both sides
6x=36
/6. /6
x=6
Hopes this helps please mark brainliest
Answer:
x = 6
Step-by-step explanation:
Given equation,
→ 6x - 16 = 20
Now the value of x will be,
→ 6x - 16 = 20
→ 6x = 20 + 16
→ 6x = 36
→ x = 36/6
→ [ x = 6 ]
Hence, the value of x is 6.
11. The equation 4 y=3 x+6 represents a line. What are the slopes of lines that are parallel and perpendicular to the given line? Drag the correct numbers into the boxes to complete the sentence.
Lines parallel to the given equation will have a slope of Drop Area , and lines perpendicular to the given equation will have a slope of Drop Area.
Slope of Parallel line is 3/4
Slope of Perpendicular line is -4/3
What is Slope of Line?
The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
Solution:
General Form of Line: y = mx + c
here, m is the slope
4y = 3x + 6
y = 3/4x + 3/2
Parallel Line have the same Slope = 3/4
Perpendicular Line:
Product of Slope = -1
Slope of Perpendicualr Line = -4/3
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help meeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeee!!!!!
Answer:
11.6 years
Step-by-step explanation:
Given
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
we can solve for [tex]t[/tex]
[tex]t=\frac{ln(\frac{A}{P} )}{n*ln(1+\frac{r}{n}) }[/tex]
We are given
[tex]A=1800\\P=900\\r=0.06\\n=12[/tex]
We can evaluate [tex]t[/tex].
[tex]t=\frac{ln(\frac{1800}{2} )}{12*ln(1+\frac{0.06}{12}) }[/tex]
[tex]t=11.6[/tex]
how do i solve this question
Answer: (x-2)(x-10)
Step-by-step explanation:
1. Factor out 3x by diving everything by it, this makes the monomial 3x(x^2-12x+20)
2. From here, you do your basic factoring and reach that the answer is (x-2)(x-10)
lmk if you need more details for explanation
Suppose the following information was collected, where x=diameter of tree trunk in inches, and y=tree height in feet
x 4 2 8 6 10 6
y 8 4 18 22 30 8
If the LSRL equation is y=-3.6 + 3.1x, what is your estimate of the average height of all trees having a trunk diameter of 7 inches?
A) 18.1
B) 19.1
C) 20.1
D) 21.2
E) 22.1
The estimate of the average height of all the trees having a trunk diameter of 7 inches is y = 18.1 feet. This is obtained by using the LSRL equation. Option A is the correct value.
What is the LSRL equation?The LSRL equation is defined as the Least squares regression line. This is the line that minimizes the variance. So, it is the best line of fit for a set of data points.
The equation is in the form of Y = a + bX
Here a is the intercept and b is the slope.
Calculation:It is given that,
X is given as the diameter of a tree trunk in inches
Y is given as the tree height in feet
The given data points are:
X: 4, 2, 8, 6, 10, 6
Y: 8, 4, 18, 22, 30, 8
For these data points, the least squares regression line is given by the equation Y = - 3.6 + 3.1X
So, the estimate of the average height of all trees having a trunk diameter of 7 inches is
Y = - 3.6 + 3.1X ⇒ Y = -3.6 + 3.1 × 7
⇒ Y = -3.6 + 21.7
∴ Y = 18.1 feet
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Andrew Industries purchased $163,000 of raw materials on account during the month of March. The beginning Raw Materials Inventory balance was $21,600, and the materials used to complete jobs during the month were $139,200 of direct materials and $12,800 of indirect materials. What is the ending Raw Materials Inventory balance for March?
The ending Raw Materials Inventory balance for March is 31,800.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.
Main Body:
We use the Inventory identity to solve for ending inventory
Beginning Inventory + Purchase = ending Inventory + used
20,800 +159,000 = ending inventory + used materials
used materials:
135,600 direct
12,400 indirect
148,000 total materials used
20,800 + 159,000 = Ending Inventory + 148,000
20,800 + 159,000 - 148,000 = Ending Inventory
Ending Inventory = 31,800
Hence the ending Raw Materials Inventory balance for March is 31,800.
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A political candidate has asked you to conduct a poll to determine what percentage of people support her.
If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed?
Give your answer in whole people.
The incumbent is the current holder of an office or position, usually in relation to an election.
Who is a political candidate?In the context of elections for public office in a representational partisan democracy, a candidate who has been selected by a political party is normally said to be the nominee of that party.Today, in 48 states, individuals participate in primaries or caucuses to elect delegates who support their presidential candidate of choice. At national party conventions, the presidential contender with the most state delegate votes wins the party nomination.This usually happens through the party's state primaries and caucuses. State delegates go to the national convention to vote to confirm their choice of candidates. But if no candidate gets the majority of a party's delegates during the primaries and caucuses, convention delegates choose the nominee.In most states, state offices include: Governor, Lieutenant Governor, Secretary of State, and Attorney General, State Supreme Court Justices, Comptroller, Treasurer, State Senators, and State Legislators.
The variable of interest is:
X: Number of people that support the candidate.
You need to calculate the sample size to estimate the population proportion of supporters given a confidence level of 99% and a margin of error of 4%
The margin of error of the confidence level for the population proportion is
d = [tex]Z_{1} - \frac{\alpha }{2} * \sqrt{\frac{p^{|}(1 - p^{|} ) }{n} }[/tex]
=[tex]\frac{d}{Z_{1}-\alpha /2 } =\sqrt{\frac{p^{2}(1-p^{2} ) }{n} }[/tex]
sample proportion "p'" since there is no sample information, nor any previous information is known, you have to consider it as the "worse case scenario" and use the value of p'= 0.50
d= 0.04
She has to take a sample of 1045 people to estimate the population proportion of her supporters with a confidence level of 99% and a margin of error of 4%
=[tex]0.5*0.5*(\frac{2.586}{0.04} } )^{2} =1044.9=1045[/tex]
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Pls help. On a number line 13 less than 8 is
Find the equation of the line.
Use exact numbers.
y= x+
Answer:
y = -2x + 5
Step-by-step explanation:
To find the slope use rise over run
To find the y-intercept see where the line intersects in the y-axis line
13 1/3 divided by 2/3
The value of expression 13 1/3 divided by 2/3 would be; 20
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the expression of 13 1/3 divided by 2/3
Therefore,
40/3 divided by 2/3
40/3 x 3/2
20
Therefore, The value of expression 13 1/3 divided by 2/3 would be; 20
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answer qauetion pls
its in the picture
Answer: 6
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Input the numbers that you are given.
|(2)(7)|−(−4) / 3 (Input the numbers)
=|14|−(−4) / 3 (Multiply your numbers, then you get 14.
=14−(−4) / 3 (find the absolute value (always will be positive) )
=18/3 (Change the fraction into a whole number)
=6
14) Huong had $23 to spend on two pens. after buying them she had $15. How much did each pen cost
Answer:
Step-by-step explanation:
23-15=8 (pour savoir combien elle a dépenser en tout)
8 diviser par 2= 4 (pour savoir le prix d'un stylo)
chaque stylo vaut 4 $
The ratio of Pablo's age to Richard's age is 6 : 7. The ratio of Pablo's age to Tristan's age is 5 : 4. Find the ratio of Pablo's age to Richard's age to Tristan's age.
Ages of Tristan, Richard, and Pablo are in the order 6:7:4.
Detailed explanation:
Pablo is six years younger than Richard, seven years older than Tristan, and five years younger than Richard.
We can multiply the ratios of Pablo's age to Richard's age and Pablo's age to Tristan's age to determine the ratio of Tristan's age to Richard's age before determining the ratio of Tristan's age to Pablo's age.
These ratios add up to 6/7 * 5/4 = 30/28.
Pablo's age to Richard's age is 6:7, thus we may multiply this ratio by the age of Richard by Tristan's age to determine the age of Pablo, Richard, and Tristan.
Thus, the ratio of Pablo's age to Richard's age to Tristan's age is 6:7:4.
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Complete a proof to solve. Given: IJKL is a parallelogram, ∠1 ≅ ∠2. Prove: IJKL is a rectangle
A rectangle is one of the types of four sided figures generally refers to as quadrilaterals. The required proof is as stated below:
Rectangles, Parallelograms, square, trapezium, kite and rhombus are a family of quadrilaterals, since they all have four straight sides. Each of these figures have individual properties that can be used to differentiate one from the other.
Some peculiar properties that can be used to identify a rectangle are:
the opposite sides have equal lengthit has two equal diagonalsadjacent sides are at an angle of [tex]90^{o}[/tex] to each otherTherefore to prove that IJKL is a rectangle;
<1 ≅ <2 (Given)
IL ≅ JK (opposite sides are equal)
IJ ≅ LK (opposite sides are equal)
IK ≅ JL (diagonals have equal length)
M is the midpoint of IK and JL respectively.
<JIK ≅ <IKL (alternate angles property)
<IJL ≅ <KLJ (alternate angles property)
IL ⊥ IJ
IJ ⊥ JK
JK ⊥ LK
LK ⊥ LI
Therefore, the given figure is a rectangle.
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You bought 8 apples at the store. The total cost was $6.00.
Let c be the cost of one apple.
Write and solve an equation to find the cost of one apple.
Answer:
Step-by-step explanation:
to put into an equation:
8c=6.00
c=6.00/8
c=$0.75
The cost of one apple is $0.75
Solve the equation for x
(x-5)/10=5
x=____
Answer:
x = 55
Step-by-step explanation:
[tex]\frac{x-5}{10}[/tex] = 5 ( multiply both sides by 10 to clear the fraction )
x - 5 = 10 × 5 = 50 ( add 5 to both sides )
x = 55
The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was ____million.
In 2000, the population of the state was 23.1 million and the population of the state reach 28.3 million in 2013
How to determine the population of the state in 2000?From the question, we have the following parameters that can be used in our computation:
A=23.1 е⁰⁰¹⁵²⁺
Also from the question, we have
The variable t represents the number of years after 2000.
This means that
t = Current year - 2000
Substitute the known values in the above equation, so, we have the following representation
t = 2000 - 2000
Evaluate
t = 0
So, we have
A=23.1 е⁰⁰¹⁵² ˣ ⁰
Evaluate the above equation
A = 23.1
When the population reaches 28.3 millionHere, we have
A = 28.3
Substitute the known values in the above equation, so, we have the following representation
23.1 е⁰⁰¹⁵²⁺ = 28.3
Divide both sides by 23.1
е⁰⁰¹⁵²⁺ = 1.22510822511
Take the natural logarithm of both sides
0.0152t = 0.203
So, we have
t = 0.203/0.0152
Evaluate
t = 13
So, the year is
Year = 2000 + 13
Year = 2013
This means that the population of the state reach 28.3 million in 2013
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Which of the following examples illustrates the law of supply?
Select the correct answer below:
When the price of housing increases, more homeowners want to sell their house.
Johnathan will not sell his car unless he can get at least $5,000 for it.
Sylvia wanted to sell all her CDs when she saw that buyers are willing to pay more for them.
all of the above
Answer:
i think it would be a; When the price of housing increases, more homeowners want to sell their house.
Which set of ordered pairs represents a linear function?
A. ((-5, -3), (-3, 5), (1, 1)}
B. ((-5, 3), (3, 0), (1,5)}
C. {(-5, 3), (3, 1), (1, 1)}
D. ((-5, -3), (-5, -1), (-5, 1)}
Answer:
C
Step-by-step explanation:
Linear Function- points on a graph that make up a straight line negative or positive.
Only Values of (C) makes a perfect line.
Write a polynomial f(x) that satisfies the given conditions
The least polynomial with degree 3 is equal to f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7.
What is the least polynomial that contains a given set of roots?
In this problem we need to determine the least polynomial such that its degree is 3 and - i 2 and 8 / 7 are roots of the resulting expression. By quadratic formula, the roots - i 2 is along with its conjugate i 2 to obtain a quadratic equation with real coefficients. The factor form of the cubic polynomial is:
f(x) = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Roots of the polynomial.And we must determine the standard form of the polynomial by means of algebra properties. This form is shown below:
f(x) = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients.
First, write the polynomial in factor form: (a = 1)
f(x) = (x - 8 / 7) · (x + i 2) · (x - i 2)
f(x) = (x - 8 / 7) · (x² + 4)
f(x) = x³ - (8 / 7) · x² + 4 · x - 32 / 7
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Kyle plans to invest $7000, part at 6% simple interest and the rest at 7% simple interest. What is the most that he can
invest at 6% and still be guaranteed at least $440 in interest per year?
Answer:
$5000
Step-by-step explanation:
Let x represent the amount invested at 6% interest. Then 7000-x is the amount invested at 7% interest
6% interest = 6/100 = 0.06 in decimal
7% interest = 7/100 = 0.07
Interest earned from depositing x dollars at 6% = 0.06x
Interest earned from depositing 7000-x at 7% = 0.07(7000-x)
Total interest earned would be
0.06x + 0.07(7000-x)
Since this must be at least $440 we get the equation interest as
0.06x + 0.07(7000-x) = 440
Simplifying
0.06x + 0.07 x 7000 - 0.07x = 440
0.06x + 490 -0.07x = 440
-0.01x = 440 - 490
-0.01x = -50
Multiply both sides by -1
==> 0.01x = 50
==> x = 50/0.01 = 5000
So max amount that can be invested at 6% interest = $5000
(NEED HELP ASPAD- WORTH 70 POINTS!)
Mr. [name] wants to order sandwiches for his class. Each sandwich, x, costs 6 dollars and there is a delivery fee of 12 dollars.
1.) Write an equation representing the cost, y, of this order of 7 sandwiches.
2.) Show your work to represent the cost of an order of 7 sandwiches.
3.)Show your work to solve how any sandwhitches you could buy with 78 dollars.
x=6
d=12
7x+12 or 7x+d
7(6) + 12 or (7x6) + 12 = 54
78-12 = 66
66/6 = 11
11x + 12 =78.
You are playing a game that involves tossing a single die. If you roll a one, you win $100. If you roll a 2, you win $50. If you roll anything else, you lose $25. What are your expected winnings?
The required probability of winning is given as 0.32.
Given that,
Playing a game that involves tossing a single die. If roll one, you win $100. If you roll a 2, you win $50. roll anything else, you lose $25.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
total number of sample spaces = 6
total of favorable outcome = 2
Probability fo the winning = 2 / 6 = 0.3333 or 0.32
Thus, the required probability of winning is given as 0.32.
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