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A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.

Part A: Find the theoretical probability of a fair coin landing on heads. (2 points)

Part B: Flip a coin 15 times and record the frequency of each outcome. (4 points)

Part C: Determine the experimental probability of landing on heads. (4 points)

Part D: Compare the theoretical and experimental probabilities. Explain your answer. (2 points)

Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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The length of NI is 8.5 cm.

The area of a kite can be found using the formula: Area = (d1 * d2)/2, where d1 and d2 are the lengths of the diagonals.

Substituting the given values, we get:

Area = (12 * 15)/2

Area = 90 square cm

Therefore, the area of the kite is 90 square cm.

In a parallelogram, opposite angles are equal. So, we have:

Angle A = Angle C (opposite angles)

Angle B = Angle D (opposite angles)

Also, sum of adjacent angles in a parallelogram is 180 degrees. So, we have:

Angle A + Angle B = 180 degrees

(x+30) + (3x-90) = 180

4x - 60 = 180

4x = 240

x = 60

Therefore, Angle A = x + 30 = 90 degrees, and Angle B = 3x - 90 = 90 degrees.

Let the shorter base of the trapezoid be x. Then, the longer base is x+6 (as given in the problem).

The median of a trapezoid is the average of the two bases. So, we have:

Median = (x + x + 6)/2 = 19

2x + 6 = 38

2x = 32

x = 16

Therefore, the shorter base of the trapezoid is 16 m and the longer base is 22 m.

In an isosceles trapezoid, opposite angles are supplementary. So, we have:

Angle C + Angle L = 180 degrees

4x + 3 + 5x - 15 = 180

9x - 12 = 180

9x = 192

x = 21.33

Therefore, the value of x is 21.33.

In a trapezoid, the median is the average of the two bases. So, we have:

AB = 18 (given)

Median = (SP + NI)/2

But SP = NI (opposite sides of a trapezoid are equal)

So, Median = 2SP/2 = SP

Therefore, SP = Median = 19/2 = 9.5 cm

Also, AB = SP + NI

18 = 9.5 + NI

NI = 8.5 cm

Hence concluded that the length of NI is 8.5 cm.

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Answer:

(4x - 9)(3x + 2)(4x - 5)(3x - 1).

Step-by-step explanation:

Let's substitute y = (12x² - 19x):

So we have y² - 13y - 90, which can be factored as:

y² - 13y - 90 = (y - 18)(y + 5)

Substituting y back:

(12x² - 19x)² - 13(12x² - 19x) - 90 = [(12x² - 19x) - 18][(12x² - 19x) + 5]

= (12x² - 19x - 18)(12x² - 19x + 5)

= (4x - 9)(3x + 2)(4x - 5)(3x - 1)

Answer:  the tank filled with water weighs 4,710 pounds.

Step-by-step explanation: where:

π = 3.14 (surmised esteem of pi)

r = span = 2 feet

h = tallness = 6 feet

V = 3.14 x (2 feet)^2 x 6 feet

V = 75.36 cubic feet

Since one cubic foot of water weighs 62.5 pounds, the weight of the water within the tank can be calculated by increasing the volume of water by its weight:

Weight of water = volume of water x weight per cubic foot

Weight of water = 75.36 cubic feet x 62.5 pounds per cubic foot

Weight of water = 4,710 pounds

1)  The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2)  CD = 2AD.

1) To prove that BMED is a trapezoid, we need to show that BM || ED.

Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).

Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).

Therefore, to show that BM || ED, it is enough to show that AC || OB.

We know that OB is a transversal to the parallel lines BM and AM, so we have:

∠OBD = ∠MBC (corresponding angles)

Similarly, we have:

∠OAD = ∠ABC (corresponding angles)

Since ∠MBC = ∠ABC (because [AM] is the median), we have:

∠OBD = ∠OAD

Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.

2) To prove that D is the midpoint of [AE], we need to show that AD = DE.

Since [AM] is the median, we have:

AD = MC

Also, since E is the midpoint of DC, we have:

DE = EC

So it is enough to show that MC = EC.

Since O is the midpoint of AM, we have:

OM = MA/2

But MA = MC + AC/2 (because [AM] is the median), so we have:

OM = (MC + AC/2)/2

= MC/2 + AC/4

Also, since E is the midpoint of DC, we have:

OE = EC/2

But AC = 2DC (because [AM] is the median), so we have:

OE = EC/2 = AC/4

Therefore, we have:

OM = OE

So triangle OME is isosceles, and we have:

∠OEM = ∠OME

But ∠OED = ∠OEM (because DE || AC), so we have:

∠OED = ∠OME

Therefore, triangles ODE and OME are similar, so we have:

OD/OM = OE/OE

= 1

Therefore, OD = OM.

But we also have:

OM = MA/2 = MC/2 + AC/4

= AD/2 + AC/4 (because [AM] is the median)

So we have:

OD = OM = AD/2 + AC/4

= AD/2 + DC/2 (because AC = 2DC)

= (AD + DC)/2

= AE/2 (because E is the midpoint of DC)

Therefore, we have shown that D is the midpoint of [AE].

Moreover, we have:

CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)

= AD + MC/2 (because [AM] is the median)

= AD + AD/2 (because AD = MC)

= 3AD/2

So we have CD = 2AD.

3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.

Since [AM] is the median, we have:

BM = MC

Also, since O is the midpoint of AM, we have:

OM = BM/2 + AM/2

= BM/2 + 2BM/2 (because [AM] is the median)

= 3BM/2

Therefore, we have:

BD = BM - MD

= MC - MD

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On solving the provided question we can say that as a result, the system of equations' solution is: x = 12.62 and y = 4/13

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions.

We wish to eliminate one of the variables, either x or y, by adding or subtracting the two equations to solve this system of equations using the elimination technique. To do this, multiply one or both equations by a constant factor such that one of the variables has the same coefficient in both equations but with opposite signs.

By multiplying the first equation by 5 and adding it to the second, we can remove x. This results in:

5x - 10y = 60

5x + 3y = -44

-13y = -4

y = 4/13

We may now plug this y value into one of the original equations to find x. Let's look at the first equation:

x - 2y = 12

x - 2(4/13) = 12

13x - 8 = 156

13x = 164

x = 12.62

As a result, the system of equations' solution is:

x = 12.62 and y = 4/13

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p-value of 0.028 is considered statistically significant at a significance level of 0.05. This suggests that we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis that the true proportion exceeds 0.75.

To calculate the p-value for this test, we need to use the standard normal distribution table or a statistical software.

First, we need to find the area under the standard normal distribution curve to the right of the test statistic of 1.91.

Using a standard normal distribution table, we can find that the area to the right of 1.91 is 0.0287 (rounded to four decimal places).

Since this is a one-tailed test (the alternative hypothesis is that the true proportion is greater than 0.75), the p-value is equal to the area to the right of the test statistic, which is 0.0287.

Therefore, the p-value for this test is 0.028 (rounded to three decimal places). This means that if the null hypothesis (that the true proportion is less than or equal to 0.75) were true, we would expect to see a test statistic as extreme as 1.91 or more extreme in only 0.028 of all possible samples.

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The p-value for the test when the test statistic is 1.91 and we are testing if the true proportion exceeds 0.75 is

approximately 0.028, rounded to 3 decimal places.

Given that the test statistic for testing, if the true proportion exceeds 0.75, is 1.91, we need to find the p-value for this

test and round it to 3 decimal places.

Identify the test statistic

The test statistic provided is 1.91.

Determine the tail of the test

Since we are testing if the true proportion exceeds 0.75, it is a right-tailed test.

Find the p-value

Using a Z-table or statistical software, find the area to the right of the test statistic (1.91) under the standard normal

distribution. This area corresponds to the p-value.

The area to the right of 1.91 in the Z-table is approximately 0.028. Therefore, the p-value for this test is approximately

0.028.

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Number of clients who do not play either the piano or the guitar is 22

To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.

Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B

|A ∪ B| = |A| + |B| - |A ∩ B|

where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments

Substituting the given values, we get

|A ∪ B| = 46 + 58 - 17

|A ∪ B| = 87

Therefore, the number of clients who do not play either instrument is:

109 - 87 = 22

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Answer:

Let's denote:

M: the set of students who like maths

S: the set of students who like science

n(M): the number of students who like maths

n(S): the number of students who like science

n(M ∩ S): the number of students who like both maths and science

n(M ∪ S): the number of students who like maths or science (or both)

We can use the principle of inclusion-exclusion to find n(M ∪ S):

n(M ∪ S) = n(M) + n(S) - n(M ∩ S)

From the problem statement, we know:

n(M) = 10

n(S) = 15

n(M ∩ S) = ? (unknown)

We also know that 10 students like neither maths nor science, which means that:

n(M ∪ S)' = 10

where (M ∪ S)' denotes the complement of M ∪ S, i.e., the set of students who do not like maths or science.

We can use the formula:

n(A') = N - n(A)

where N is the total number of students (N = 50).

n(M ∪ S)' = n((M ∪ S))' = N - n(M ∪ S) = N - (n(M) + n(S) - n(M ∩ S))

Substituting the known values:

n((M ∪ S))' = 50 - (10 + 15 - n(M ∩ S)) = 25 + n(M ∩ S)

Simplifying:

n(M ∩ S) = n((M ∪ S))' - 25 = 10

Therefore, we have:

n(M ∪ S) = n(M) + n(S) - n(M ∩ S) = 10 + 15 - 10 = 15

The ratio of the students who like maths or science is:

n(M ∪ S) / N = 15 / 50 = 3/10

So the required ratio is 3:10.

Step-by-step explanation:

The electrician needs approximately 296.26 feet of wire.

The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).

The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.

Using trigonometry, we can write:

sin(17°) = opposite / hypotenuse

where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:

hypotenuse = opposite / sin(17°)

To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:

tan(17°) = opposite / 85

Solving for the opposite side, we get:

opposite = 85 tan(17°)

Substituting this into the formula for the hypotenuse, we get:

hypotenuse = (85 tan(17°)) / sin(17°)

hypotenuse ≈ 296.26 feet

Therefore, the electrician needs approximately 296.26 feet of wire.

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The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.

Option C is the correct answer.

We have,

Given ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53

Mean without the additional teacher

= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 51 + 52 + 53) / 12

= 37.5

New ages: 24, 32, 33, 35, 41, 42, 42, 43, 44, 51, 52, 53, 45

Mean with the additional teacher

= (24 + 32 + 33 + 35 + 41 + 42 + 42 + 43 + 44 + 45 + 51 + 52 + 53 + 45) / 13

= 582/13

= 44.77

= 45

Therefore,

The mean would increase in value to about 45 when the teacher with the age of 45 is added to the data.

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Answer:

2((6(14) + 6(5) + 14(5)) = 2(84 + 30 + 70) =

2(184) = 368 square centimeters

Answer: 1.7(repeating) OR 1.78

Step-by-step explanation:

Divide 4 by 2.25 (2 1/4)

The calculated volume of the figure is 761.97 cubic inches

From the question, we have the following parameters that can be used in our computation:

The volume of the figure is calculated as

Volume = Cylinder + Cone - Hollow cylinder

So, we have

Volume = 3.14 * (8/2)^2 * 18 + 1/3 * 3.14 * (8/2)^2 * 5 - 3.14 * (2)^2 * 18

Evaluate

Volume = 761.97

Hence, the volume is 761.97 cubic inches

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The probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 8 + 7 + 6 = 21

probability of picking a blue ball = 7/21

probability of picking a green ball = 6/21

probability of picking a blue or green ball = 7/21 + 6/21

probability of picking a blue or green ball = (7 + 6)/21

probability of picking a blue or green ball = 13/21

probability of picking a blue or green ball = 0.6190

Therefore, the probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

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The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.

The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.

It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.

A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.

The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.

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The two data sets that meet the given conditions for in centers, and variability is in the explanations.

Data Set 1 - Heights of Adults in a City:

Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62

Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.

Data Set 2 - Salaries of Employees in a Corporation:

Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55

Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.

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A=200in² is the area of the shaded polygon so 200in² ➗ 30in

The cost of the treat would be 40 pennies.

In mathematics, an expression is a combination of symbols (such as numbers, variables, and operations) that represents a value.

Expressions can be as simple as a single number or variable, or they can be more complex, involving multiple operations and variables. They can also include functions, exponents, and other mathematical concepts.

Chloe started with 74 pennies and lost 10, so she has 74 - 10 = 64 pennies left. The treat costs 5/8 of her remaining pennies,

Calculate the cost by multiplying 5/8 by 64:

(5/8) x 64 = 40

Therefore, the treat costs 40 pennies.

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Answer: f(8) = -208

Step-by-step explanation:

     To solve, we will substitute 8 into the equation for x.

Given:

     f(x) = -3x² - 2x

Substitute 8 for x:

     f(8) = -3(8)² - 2(8)

Square:

     f(8) = -3(64) - 2(8)

Multiply:

     f(8) = -192 - 16

Subtract:

     f(8) = -208

Answer: 3,456

Step-by-step explanation:

The matrix of dependent coefficients and the vector column of independent variables of the system of linear equations are:

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

In this question we find a representation of a system of three linear equations with three variables {x, y, z}. This system can be described by following expression according to linear algebra:

[tex]\vec A \,\bullet \,\vec x = \vec B[/tex]

Where:

Please notice that operator "•" represents a dot product.

Then, the matrix of dependent coefficients and the vector column of independent variables are, respectively:

Matrix of dependent coefficients

[tex]\vec A = \left[\begin{array}{ccc}1&-2&3\\-4&5&-6\\7&-8&9\end{array}\right][/tex]

Vector column of independent variables

[tex]\vec {b} =\left[\begin{array}{ccc}6\\8\\1\end{array}\right][/tex]

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The perimeter of rectangle JKLM which has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2) On the coordinate plane is 30 units.

By applying the Pythagorean distance formula we calculate the length of each side of the rectangle as,

Distance, d = √{(x₁ - x₂)² + (y₁ - y₂)²}  (units)

where  (x₁, y₁ ) and ( x₂, y₂) are the coordinates of both the end of a side of the rectangle.

The coordinates of the rectangle JKLM are given as J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2).

Thus,

| JK | = √{(-2 - 6)² + (2 +4)²} = 10 units

| JM | = √{( -2 +5)² + (2 +2)²} = 5 units

| KL | =√{(6-3 )² + (-4+8 )²} = 5 units

| LM | = √{(3+5)² + (-8+2)²} = 10 units

Therefore,  JK and LM are sides opposite to each other (and let it be length) and JM and Kl are the other pair (and let it be the breadth) in the rectangle.

Thus, perimeter of a rectangle can be found with the formula,

Perimeter of JKLM = 2( length + breadth) in units

= 2(10+ 5) units

= 30 units

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1. The numeric values of the function are given as follows:

2. As x approaches negative infinity, y approaches zero.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The numeric values for this problem are given as follows:

Increasing the negative exponent, the number gets closer to zero.

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according to the given question Anna scored highest in the Afrikaans test.

When a relationship consistently has the same ratio, it is considered to be proportionate. For instance, the average amount of apples grown on each tree determines the number the trees within a fruit orchard plus the quantity of apples harvested. In mathematics, a linear relationship between two numbers or variables is referred by the term being proportionate. The other amount doubles when the initial amount does. The other variables also decline when one variable is brought down to 1/100th of its prior value.

given,

To determine whether Anna's results are proportionate, we need to compare the percentage scores she received in each test.

For the Afrikaans test, Anna's percentage score is (22/30) x 100% = 73.33%

For the mathematical literacy test, Anna's percentage score is (18/25) x 100% = 72%

Since Anna's percentage score for the Afrikaans test is higher than her percentage score for the mathematical literacy test, her results are not proportionate. Therefore, Anna scored highest in the Afrikaans test.

Note that if we were to compare the raw scores (22 vs. 18), it would seem like Anna performed better in the Afrikaans test. However, since the two tests have different total marks (30 for Afrikaans and 25 for mathematical literacy), comparing the raw scores directly does not give a fair comparison. Instead, we need to compare the percentage scores, which take into account the total marks of each test.

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Answer:

The length of the diagonal from P to Q is

[tex] \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17[/tex]

The correct statements  to conclude that a parallelogram is a rhombus are:  a.)  Segment AD ≅  Segment AB  e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are  the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.  

To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.  

The correct statements  to conclude that a parallelogram is a rhombus are:

a.)  Segment AD ≅  Segment AB

e.)  Segment AB ≅  Segment DC

f.) ∠ABC ≅ ∠CDA

These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.

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The drive-thru that typically has more wait time is

Burger Quick, because it has a larger median.

Option A is correct.

Because Burger Quick's box plot displays a higher interquartile range (from 9.5 to 24) than Super Fast Food (from 8.5 to 15.5), Burger Quick often has longer wait times.

Additionally, Burger Quick's median (15.5) is greater than Super Fast Food's median (12), demonstrating that Burger Quick's middle value of reported wait times is higher than Super Fast Food's middle value of reported wait times.

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Answer:

0.75

Step-by-step explanation:

P (Cherry or Orange)

0.27 + 0.20 = 0.47

P (Not Strawberry)

0.27 + 0.28 + 0.20 = 0.75