Suppose that in the maintenance of a large medical-records file for insurance purposes the probability of an error in processing is 0.0010, the probability of an in filing is 0.0009, the probability of an error in retrieving is 0.0012, the probability of an error in processing as well as filing is 0.0002, the probability of an error in processing as well as retrieving is 0.0003, and the probability of an error in processing and filing as well as retrieving is 0.0001. What is the probability of making at least one of these errors? (P(R intersection F)=0.0002) Be sure to draw a Venn diagram.

Answer:

Step-by-step explanation:

Based on what you have here as the slope we can set the slope formula equal to 34 using the points (0, 8) and (8, c) to solve for c, then use the points (0, 8) and (a, 5) to solve for a.  

c first:

[tex]\frac{c-8}{8-0}=34[/tex] and

[tex]\frac{c-8}{8}=34[/tex] and

c - 8 = 272 s0

c = 280

For a:

[tex]\frac{5-8}{a-0}=34[/tex] and

[tex]\frac{-3}{a}=34[/tex] and

-34a = 3 so

[tex]a=-\frac{3}{34}[/tex]

That seems a little weird, but when you plug those points into the slope formula to solve for the slope, it works out the way it should.

Answer:

The average rate of change is $25.5 per hour, option B.

Step-by-step explanation:

Average Rate of Change

When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from [tex]x=x_1[/tex] to [tex]x=x_2[/tex]. It can be computed as the slope of a line .

[tex]\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}[/tex]

The provided function is

[tex]C(x)=25.50x + 50[/tex]

We are required to compute the average rate of change between the points

[tex]x_1=3\ ,\ x_2=9[/tex]

Let's compute

[tex]C(3)=25.50(3) + 50=126.5[/tex]

[tex]C(9)=25.50(9) + 50=279.5[/tex]

[tex]\displaystyle m=\frac{279.5-126.5}{9-3}[/tex]

[tex]\displaystyle m=\frac{153}{6}=25.5[/tex]

The average rate of change is $25.5 per hour, option B.

Answer:

time series

Step-by-step explanation:

A time series is a sequence of observations on a variable measured at successive points in time or over successive periods of time.

Answer:

Option (4) is the answer.

Step-by-step explanation:

The given question is without options ; here is the complete question.

Myriah wants to use dimensional analysis to find out how many centimeters (cm) are in 1.4 meters (m). Which of these equalities will be useful for this calculation?

2.54 cm = 1 in.

1 m = 39.37 in.

1 cm = 10 mm

100 cm = 1 m

During the dimensional analysis Myriah wants to convert the dimension from meter to centimeter.

Option (1), In this option given equality is to convert centimeter to inch. which is not required.

Option (2), In this option equality is to convert meter to inch which is not required.

Option (3) the equality given will convert cm to mm, which is not required.

Option (4) equality given in this option will convert meter to centimeter which is the required equality.

Therefore, Option (4) will be the answer.

If the cutting plane was parallel to the circular base of the cones, then we would have a circular cross section (assuming the plane doesnt cut through the vertex). However, we're told than the plane intersects both nappes, or cones, so it's not possible for the plane to be parallel to the base faces. We can rule out choice A.

We can rule out choice C and choice D for similar reasons. An ellipse only forms if the plane only cuts through one cone only, which is the same story for a parabola as well.

Answer:

  y = 33°

Step-by-step explanation:

The left side and the right side are parallel, so the angles marked y and 33° are alternate interior angles, hence congruent.

  y = 33°

Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️

Step-by-step explanation:

Let B the cost of a pair of boots and let T the cost of a pair of tennis shoes.

Then we know:

A pair of boots and a pair of tennis shoes cost $196.12:

B + T = $196.12 } Equation 1

We also know:

The difference in their cost is $44.38:

B - T = $44.38 } Equation 2

From the equation 1 we know T:

T = $196.12 - B

Now we can substitute this value in equation 2:

B - ($196.12 - B) = $44.38

B - $196.12 + B = $44.38

2B = $44.38 + $196.12 = $240.5

B = $240.5/2 = $120.25◄cost of a pair of boots

Since we know the value of T from the equation 1:

T = $196.12 - B = $196.12 - $120.25 = $75.87◄cost of a pair of tennis shoes

Answer: A pair of boots costs $120.25. A pair of tennis shoes costs $75.87✔️

We can substitute these values in equations 1 and 2 and check the results:

B + T = $196.12 } Equation 1

$120.25 + $75.87 = 196.12 ✔️check!

B - T = $44.38 } Equation 2

$120.25 - $75.87 = $44.38 ✔️check!

Spymore

The cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a pair of boots and a pair of tennis shoes cost $196.12.

Let the cost of a pair of boots be b and the cost of a pair of tennis shoes be t.

Now, b+t=196.12 --------(I)

The difference in their cost is $44.38.

b-t=44.38 --------(II)

Add equation (I) and (II), we get

b+t+b-t=196.12+44.38

2b=240.5

b=240.5/2

b=$120.25

Substitute b=$120.25 in equation (I), we get

b+t=196.12

t=196.12-120.25

t=$75.87

Therefore, the cost of a pair of boots is $120.25 and the cost of a pair of tennis shoes is $75.87.

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Final answer:

To find the probability that A.J. and M.J. finish their jobs within a certain time, we need to calculate the z-score for the given values and use a standard normal distribution table or a calculator to find the probability.

Explanation:

(a) To find the probability that A.J. finishes in less than 900 minutes, we need to calculate the z-score (standard score) for the value 900 using the formula: z = (x - mean) / standard deviation. In this case, x = 900, mean = 50 minutes, and standard deviation = 10 minutes. Once we have the z-score, we can use a standard normal distribution table or a calculator to find the probability.

(b) To find the probability that M.J. finishes in less than 900 minutes, we use a similar process as in part (a), but with different mean and standard deviation values. In this case, x = 900, mean = 52 minutes, and standard deviation = 15 minutes.

(c) To find the probability that A.J. finishes before M.J., we can compare the means of the two distributions. Since A.J.'s mean is lower than M.J.'s mean, the probability of A.J. finishing before M.J. is higher.

Answer

Cluster sampling. See explanation below.

Step-by-step explanation:

For this case they not use random sampling since we are selecting people from flights. Because we select just 5 random flights.

Is not stratified sampling since we don't have strata clearly defined on this case, and other important thing is that in order to apply this method we need homogeneous strata groups and that's not satisfied on this case.

Is not convenience sampling because they NOT use a non probability method in order to select the people from the flights.

So then the only possible method is cluster sampling since we have clusters clearly defined (Passengers from the airlines), and we satisfy the condition of homogeneous characteristics on the clusters and an equal chance of being a part of the sample, since we are selecting RANDOMLY, the 5 flights to take the information.

Answer:

Step-by-step explanation:

let x be the length of third side.

10-5<x<10+5

or 5<x<15

so third side is between 5 and 15 .

Answer:  The length of the third side is greater than 5 and less than 15 units.

Step-by-step explanation: Given that the lengths of two sides of a certain triangle are 5 and 10 units.

We are to find the length of the third side of the triangle.

Let x represents the length of the third side of the given triangle.

We know that the sum of the lengths of two sides of a triangle is always greater than the length of the third side, so we must have

[tex]5+10>x\\\\\Rightarrow x<15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

[tex]5+x>10\\\\\Rightarrow x>5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

and

[tex]x+10>5\\\\\Rightarrow x>-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

From inequalities (i), (ii) and (iii), we get

[tex]5<x<15.[/tex]

Thus, the length of the third side is greater than 5 and less than 15 units.

Answer:

C

Step-by-step explanation:

One angle is larger than other from the SAS Inequality Theroem that state that if two congruent sides are congruent, then one of the included angle is greater than the other

Answer

m< 1 > m < 2.

Step-by-step explanation:

< 1 is opposite the longer side.

Answer:

a) A response of 8.9 represents the 92nd ​percentile.

b) A response of 6.6 represents the 62nd ​percentile.

c) A response of 4.4 represents the first ​quartile.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5.9

Standard Deviation, σ = 2.2

We assume that the distribution of response is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

a) We have to find the value of x such that the probability is 0.92

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<1.405) = 0.92[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9[/tex]

A response of 8.9 represents the 92nd ​percentile.

b) We have to find the value of x such that the probability is 0.62

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<0.305) = 0.92[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6[/tex]

A response of 6.6 represents the 62nd ​percentile.

c) We have to find the value of x such that the probability is 0.25

P(X < x)  

[tex]P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(z<0.305) = -0.674[/tex]

[tex]\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4[/tex]

A response of 4.4 represents the first ​quartile.

Answer:

The Statements which are true are:

(2)(6) > (–2)(2)

6/-2 < -2/-2

6/2 > -2/2

Step-by-step explanation:

Given:

6 > –2

We need to check all options which are true,

Hence we will check for all 1 by 1.

(2)(6) > (–2)(2)

It means that when 2 is multiplied on both side we get the value as

12 > -4

Since 12 is greater than -4.

Hence this statement is true.

6/2 < -2/2

It means that when 2 is divided on both side we get the value as

3 < -1

Since 3 is greater than -1.

Hence this statement is false.

(–2)(6) > (–2)(–2)

It means that when -2 is multiplied on both side we get the value as

-12 > 4

Since -12 is less than 4.

Hence this statement is false.

6/-2 < -2/-2

It means that when -2 is divided on both side we get the value as

-3 < 1

Since -3 is lesser than 1.

Hence this statement is true.

5) (2)(6) < (–2)(2)

It means that when 2 is multiplied on both side we get the value as

12 < -4

Since 12 is greater than -4.

Hence this statement is False.

6/2 > -2/2

It means that when 2 is divided on both side we get the value as

3 > -1

Since 3 is greater than -1.

Hence this statement is True.

Answer:

A,D,F

Step-by-step explanation:

I got these correct!

Answer:

(a) statistic

Step-by-step explanation:

The researcher conducted the research using sample space of 25 three-year-old girls and 25 three-year-old boys. This sample space is subjected to test with an expected outcome. The test allows the research to perform analysis on the event base on data he has collected. The collection, analysis and interpretation of data is called statistics.

Answer:

The answer to your question is below

Step-by-step explanation:

1)  Given

2)  Subtraction property of equality (because we are subtracting the same quantity on both sides).

3) Simplification

4) Subtraction property of equality ( because we are subtracting the same quantity on both sides).

5) Simplification

6) Multiplication property of equality (because we are multiplying the same quantity on both sides).

7) Simplification

Final answer:

The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60, calculated by adding the GST and the tip amount to the original bill.

Explanation:

To calculate the total cost of the meal including tax and tip, we add both the Goods and Services Tax (GST) and the tip percentage to the original bill amount.

The total cost, including a 5% GST and a 15% tip on a bill of $123, would be $147.60.

Answer:

[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]

So for this case the best answer would be:

d. 218’

Step-by-step explanation:

Previous concepts

Foot front : "Is a foot measured along the front of a piece of property".

Solution to the problem

For this case we need to begin finding the number of frontage feet, with the following formula:

[tex]Frontage fronts=\frac{Amount paid}{Unitary price}[/tex]

And for this case if we replace the values given we got:

[tex]Frontage fronts=\frac{100000}{250}=400 fromtage foot[/tex]

Now we need to convert the area to square feet. And we know that:

[tex] 1 acre= 43560 ft^2[/tex]

And converting we got: [tex]2 acre *\frac{43560 ft^2}{1 acre}=87120 ft^2[/tex]

Now we can divide the total area by the total of frontage feer and we got:

[tex] Depth = \frac{Area}{# frontage feet}= \frac{87120 ft^2}{400}=217.8 \approx 218[/tex]

So for this case the best answer would be:

d. 218’

Answer:

The supply and demand curves will shift to the left i.e. there will be a decrease in demand and supply.

Step-by-step explanation:

First: Tax is a compulsory contribution to state revenue, levied by the government on workers' income and business profits, or added to the cost of some goods, services, and transactions.

Secondly: Money supply is the total amount of monetary assets available in an economy at a specific time.

When tax is increased, this means individuals and businesses have to contribute more to the state revenue leaving both categories with lesser income or profit i.e. lesser to spend.

In the same way, when money supply decreases, there is lesser money available to both individuals and businesses

What this implies is that demand will decrease because income has decreased. Supply will also decrease because producers will not make as much profit given the increase in tax (tax is considered cost of production).

As a result of this, the demand curve shifts to the left, the supply curve also shift to the left because both demand and supply will decrease.

Answer:

lt is the graph of x2+3x-4

Answer:

See Graph

Step-by-step explanation:

Find the Solution for

1x2+3x−4=0

using the Quadratic Formula where

a = 1, b = 3, and c = -4

x=−b±sqrtb^2−4ac/2a

x=−3±sqrt3^2−4(1)(−4/2(1)

x=−3±sqrt9−−16/2

x=−3±sqrt25/2

Simplify the Radical:

x=−3±sqrt5/2

We get x=22x=−82

which becomes

x=1

x=−4

Here is the graph:

Answer: the slope of the line is 2

Step-by-step explanation:

The equation of a straight line is represented in the slope intercept form as

y = mx + c

Where

m = slope

c = intercept

The given equation is y = 2x + 4

Comparing it with the slope intercept form given above,

m = 2. Therefore, the slope of the line is 2

Final answer:

About 95% of households would typically be expected to have a number of cars within 2 standard deviations of the mean, as per the empirical rule for a normal distribution.

Explanation:

The question, in a broad sense, relates to the concept of a probability distribution, specifically to the normal distribution and the empirical or 68-95-99.7 rule. To answer the question about the percentage of households with a number of cars within 2 standard deviations of the mean, one needs to apply the properties of the normal distribution. Typically, about 95% of observations can be found within 2 standard deviations of the mean on a normal distribution. However, to be precise for this case, one would calculate the mean (μ) and standard deviation (σ) of the given probability distribution, then sum the probabilities of the random variable X falling between μ - 2σ and μ + 2σ to find the desired percentage of households.

About 93% of households have a number of cars within 2 standard deviations of the mean.

To determine the percentage of households that have a number of cars within 2 standard deviations of the mean, we need to perform the following steps:

       [tex]\mu = \sum xP(X=x)[/tex]

       [tex]\mu = 0(0.09) + 1(0.36) + 2(0.35) + 3(0.13) + 4(0.05) + 5(0.02) = 1.75[/tex]

       [tex]\sigma^2 = \sum (x - \mu)^2 P(X=x)\\\sigma^2 = (0 - 1.82)^2(0.09) + (1 - 1.82)^2(0.36) + (2 - 1.82)^2(0.35) + (3 - 1.82)^2(0.13) + (4 - 1.82)^2(0.05) + (5 - 1.82)^2(0.02) = 1.1675[/tex]

       [tex]\[\sigma = \sqrt{1.0764} \approx 1.0805[/tex]

      The range is from μ - 2σ to μ + 2σ.

       μ - 2σ =  1.75 - 2(1.0805) ≈ -0.411

       μ + 2σ = 1.75 + 2(1.0805) ≈ 3.911

      Since the number of cars cannot be negative, the range is from 0 to 3.911 (practically up to 3 cars).

      0.09 + 0.36 + 0.35 + 0.13 = 0.93

Thus, about 93\% of households have a number of cars within 2 standard deviations of the mean.

Complete question:

Choose an American household at random and let the random variable X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars.

Number of cars:   0\\       1 \\      2\\      3 \\     4\\       5

Probability:        0.09 \\ 0.36\\ 0.35\\ 0.13\\ 0.05\\ 0.02

About what percentage of households have a number of cars within 2 standard deviations of the mean?

Answer:

60 lines can be typed in the page

Step-by-step explanation:

Given:

Length of the page  = 17 inches

Length of the margin = 0.5-inch

length of one line  = 4/15

To Find:

The number of lines that can be typed on a page

Solution:

Let the number of line  that can be typed be  n

then

n <= [tex]n \leq \frac{\text { total length of the page}-\text {top margin} - \text{ bottom margin}}{\text{size of each line }}[/tex]

the top and bottom margins are 0.5 inches each

so we will be having

=> [tex]n \leq \frac{17 -0.5-0.5}{\frac{4}{15}}[/tex]

=>[tex]n \leq \frac{16}{\frac{4}{15}}[/tex]

=>[tex]n \leq \frac{16\times 15}{4}[/tex]

=>[tex]n \leq\frac{240}{4}[/tex]

=> [tex]n \leq 60[/tex]

Answer:

a)20$

b)46,1$

c)0,3336

d)No concerns

Step-by-step explanation:

A) To find expected difference of cost of medical care for dogs and cats we can simply subtract average costs of cats and dogs.

[tex]120-100=20[/tex]

Expected difference will be 20$.

B) To find the standard deviation of that difference, we need to square deviations and add them and square root it again.

[tex]\sqrt{(30^2+35^2)} =46,1[/tex]

Expected difference will be 46,1$.

C)We need to find the Z value to find the probability of more expensive dogs than cats in a Vet vise.[tex]Z=(0-20)/46,1=-0,434[/tex]

Z value of the function is -0,434

From the Z table that you can find at the attachment. The probability is %33,36 or 0,3336

D) This is a subjective part. I don't have any concerns

Answer:

  ? = 47°

Step-by-step explanation:

The angle marked B at the intersection of the secants is half the difference of the arcs they intercept.

  ∠B = (DE -AC)/2 = (142° -48°)/2 = 47°

The unknown angle is 47°.

Answer:

The answer is option is (4) y ≤ 14

Step-by-step explanation:

The given function, y = - 0.5[tex](x + 10)^{2} + 14[/tex]

We have to find the range of this function. If we take the first part of the function alone we can see that it is always negative or zero. So the maximum value of the function is 14.

This happens when we make the first part zero and for that we put x = -10.

So the maximum value of the function occurs at x = -10 and that value is y = 14.

Hence the range is y ≤ 14.

The answer is option is (4) y ≤ 14

Answer:

1. 9 hours      2. $377     3. 48 hours     4. 235 feet

Step-by-step explanation:

In all cases below, let x represent the variable sought for.

1: 2x/5=3.6,

x=5/2 *3.6=9 hours

2. x-83=294

x=83+294=377

3. x+x/3=4x/3=64

x=64*3/4=48 hours

4. If the gardenview hotel's height  is x, then (x+17)/2 will be the height of the Plaza Hotel.

The combined height  will be x + (x+17)/2 = 361 feet

Multiplying by 2 across board,

2x+x+17=722

3x+17=722

3x =722-17=705

x=705/3=235m

Answer:

It is A. my friend

Step-by-step explanation:

Answer:

D. [tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]

Step-by-step explanation:

Given:

Let us find the equations of the lines from the graph.

First let us determine the equation of the broken line.

The slope of the broken line is positive as 'y' values increases with increase in 'x'. The slope is the ratio of the absolute value of y-intercept to that of the x-intercept.

x-intercept = 6, |y-intercept| = |-4| = 4

So, [tex]m=\frac{4}{6}=\frac{2}{3}[/tex]

Now, equation of a line with slope 'm' and y -intercept 'b' is given as:

[tex]y=mx+b[/tex]

Here, [tex]m=\frac{2}{3},b=-4[/tex].So, equation of the broken line is:

[tex]y=\frac{2}{3}x-4[/tex]

Now, from the graph, the solution is below the broken line. So, the equality sign is replaced by the less than inequality sign. So,

[tex]y<\frac{2}{3}x-4[/tex]

Now, let us determine the equation of the other line.

y-intercept, [tex]b = 2[/tex], x-intercept = 1

Slope is negative as 'y' decreases with increase in 'x'. So,

Slope, [tex]m=-\frac{2}{1}=-2[/tex]

Now, equation is given as:

[tex]y=-2x+2[/tex]

From the graph, the solution region is to the left of the line. So, the 'equal to' sign is replaced by the 'greater than or equal to' sign' as the line is also included in the solution region. So, the inequality becomes:

[tex]y\geq-2x+2[/tex]

Therefore, the last option is correct.

[tex]y<\frac{2}{3}x-4\ and\ y\geq-2x+2[/tex]

Answer:

A. increase the sample size

Step-by-step explanation:

By increasing sample size, the amount of data included in the statistical calculation is more. As the size increases, the uncertainty decreases, hence the confidence level on our estimate is higher. By having more sample, we have more accurate analysis, and our margin of error can be reduced as well.

Answer: [tex]\dfrac{15}{17}[/tex]

Step-by-step explanation:

Total number of cards in a deck = 52

Number of red cards = 26

Number of cards not red =

Number of ways to draw not red cards = [tex]^{26}C_3[/tex]

Total ways to draw 3 cards = [tex]^{52}C_3[/tex]

The probability that none of three cards are red = [tex]\dfrac{^{26}C_3}{^{52}C_3}[/tex]

[tex]=\dfrac{\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{3!(52-3)!}}[/tex]  [∵ [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]

[tex]=\dfrac{\dfrac{26\times25\times24\times23!}{(23)!}}{\dfrac{52\times51\times50\times49!}{3!(49)!}}=\dfrac{2}{17}[/tex]

Now , the probability that at least one of the cards drawn is a red card = 1- Probability that none cards are red

[tex]=1-\dfrac{2}{17}=\dfrac{17-2}{17}=\dfrac{15}{17}[/tex]

Hence, the required probability = [tex]\dfrac{15}{17}[/tex]

Answer:

[tex]\frac{25}{102}[/tex].

Step-by-step explanation:

Total number of cards in a deck = 52

number of black cards in a deck = 26

Find the probability that both cards are black (without replacement).

Therefore, both events are dependent.

The probability of first card is black = [tex]P_{1}=\frac{26}{52}[/tex]

the probability of second card is black = [tex]P_{2}=\frac{25}{51}[/tex]

[tex]P=\frac{26}{52}[/tex] × [tex]=\frac{25}{51}[/tex]

   = [tex]\frac{1}{2}[/tex] × [tex]\frac{25}{51}[/tex]

   = [tex]\frac{25}{102}[/tex]

The probability that both cards are black is [tex]\frac{25}{102}[/tex].

The probability that both cards picked without replacement are black is [tex] \frac {25}{102}[/tex]

Number of black cards in deck = 26

Total number of cards = 52

Recall :

Probability = (required outcome / Total possible outcomes)

Therefore,

Ist pick :

P(black card) = 26/52

Number of black cards left = 26 - 1 = 25

Total number of cards left = 52 - 1 = 51

2nd pick:

P(black card) = 25 / 51

Therefore, probability that both cards are black is ;

[tex]P(Both \: black) = \frac{26}{52} \times \frac{25}{51} = \frac {25}{102}[/tex]

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