Suppose a drawer contains six white socks, three brown socks, and seven black socks. We draw one sock from the drawer and it is equally likely that any one of the socks is drawn. We reach into the drawer looking to pull out four socks. What is the probability that we get at least two socks of the same color?
Answers
Answer:
The probability is \(1\).
Step-by-step explanation:
We have a drawer that contains :
Six white socksThree brown socks Seven black socksLet's define the following events :
W : '' The sock we got was white ''
Br : '' The sock we got was brown ''
Bl : '' The sock we got was black ''
We can calculate the following probabilities by counting :
\(P(W)=\frac{6}{16}\)
Because there are 6 white socks out of 16 socks in the drawer
Using the same reasoning :
\(P(Br)=\frac{3}{16}\)
\(P(Bl)=\frac{7}{16}\)
Now to calculate the probability of getting at least two socks of the same color we need to think about the following :
Getting at least two socks of the same color means getting two, three or four (except the brown socks because we only have three brown socks) of the same color.
Again we can calculate the probability by counting :
\(\frac{FavorableCases}{TotalCases}\)
But giving that we pull out four socks, we always will get at least two socks of the same color.
In the most desfavorable case we will get one white sock, one brown sock and one black sock. And in the last extraction we will complete it with a white, brown or black sock (obtaining two socks of the same color).
Finally, all extractions of four socks will have at least two of the same color.
The probability is \(1\).
Related Questions
How do you know that segment AD is congruent to segment BC ? Lesson (2-1)
Answers
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
What are congruent Triangles ?If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.
What are Two congruent Sides ?Two sides that are the same length make up an isosceles triangle .In addition, it contains two equal-sized angles located across from the two sides of equal length. A triangle with three identical sides is called an equilateral triangle.
So
According to the given information
Segment AD = Segment BC
Two line segments are said to be congruent if, regardless of their orientation or position, their lengths are the same.
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HELP!!!!!!!! Which system of linear equations can be solved using the information below?
Answers
The system of linear equations that can be solved from the matrices is given as follows:
-5x + 4y = 3.-8x + y = -6.How to obtain the system of equations?Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:
A = [-5 4; -8 1]
Hence the multiplication of matrices representing the system is given as follows:
[-5 4; -8 1][x; y] = [3; -6]
Applying the multiplication of matrices, the system of equations is given as follows:
-5x + 4y = 3.-8x + y = -6.More can be learned about a system of equations at https://brainly.com/question/13729904
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4(-8x + 5) - (-33x -26) =
Answers
Answer:
x = - 46
Step-by-step explanation:
See photo for step by step process. Correct me if I'm wrong. I hope it helps.
Every 2 centimeters on a floor plan represents
meters of the house. The dining room is 8 cm by
10 cm on the floor plan, and the bedroom is 6cm by10cm on the floor plan. If installing tile costs $34
per square meter and installing carpet costs $21 per
square meter, how much would it cost to install tile
in the dining room and install carpet in the bedroom?
Show your work.
Answers
Given statement solution is :- It would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.
Given:
Every 2 centimeters on the floor plan represents 1 meter of the house.
Dining Room:
On the floor plan, the dining room is 8 cm by 10 cm.
Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.
The area of the dining room is 4 meters * 5 meters = 20 square meters.
Bedroom:
On the floor plan, the bedroom is 6 cm by 10 cm.
Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.
The area of the bedroom is 3 meters * 5 meters = 15 square meters.
Now, let's calculate the costs.
Cost of Tile:
The cost of installing tile is $34 per square meter.
The area of the dining room is 20 square meters.
Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.
Cost of Carpet:
The cost of installing carpet is $21 per square meter.
The area of the bedroom is 15 square meters.
Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.
Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.
For such more questions on Cost of tile and carpet.
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After drawing a square on the board, Mr. Hinkle asked his class to identify the shape. Timothy stated that Mr. Hinkle had drawn a rhombus. Which of the following statements is true?
Answers
A survey of all beings on planet Gespil found that 18 beings preferred rew juice to all other juices. If 30 beings were surveyed altogether, what percent of them preferred rew juice?
Answers
we divide those who prefer rew juice by the total
\(\begin{gathered} \frac{18}{30} \\ =\frac{3}{5} \end{gathered}\)to find the percentage we multiply with 100
\(\begin{gathered} \frac{3}{5}\times100 \\ =60 \end{gathered}\)60%
A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The survey reported a confidence interval that between 22% and 32% of the residents supports the plan. What is the margin of error on the survey? Do not write ± ± on the margin of error.
Answers
Answer:
\(\Huge \bold{\boxed{\boxed{\text{5\%}}}}\)
Step-by-step explanation:
To calculate the margin of error for the survey, we need to use the formula:
\(\large \text{Margin of error} = \large \text{$\frac{\text{Range of values}}{2}$}\)
The range of values is the difference between the upper and lower bounds of the interval. In this case, the lower bound is 22% and the upper bound is 32%, so the range of values is:
\(\large \text{Range of values = 32\% - 22\% = 10\%}\)
Substituting this value into the formula, we get:
\(\large \text{Margin of error = $\frac{10\%}{2}$ = 5\%}\)
Therefore, the margin of error on the survey is 5%.
427 × 1,000 jnjnnjnjnnjjjjjjjjjjjjjjjjjj
Answers
Answer:
427,000...
Step-by-step explanation:
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In a study, a random sample of 2625 US adults were asked whether they agree or disagree that there is "only one true love for each person." The response and gender of the participants is shown in Table 1.
Male Female Total
Agree 372 363 735
Disagree 807 1005 1812
Don't know 34 44 78
Total 1213 1412 2625
Table 1 Is there only one true love for each person?
(a) Use the information in the table to construct a confidence interval for the difference in the proportion who agree, between males and females, using the fact that the standard error for the difference is .
Round your answers to three decimal places.
The 95% confidence interval is
to
.
(b) Is it plausible that there is no difference between males and females in the proportion who agree that each person has only one true love?
Answers
Using the information given, it is found that:
a.
The standard error for the difference is of 0.0176.
The 95% confidence interval is 0.0151 to 0.0841.
b.
Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.
What is the distribution of differences for the proportion of males and females?
For males, we have that:
\(n = 1213, p_M = \frac{372}{1213} = 0.3067, s_M = \sqrt{\frac{0.3067(0.6933)}{1213}} = 0.01324\)
For females, we have that:
\(n = 1412, p_F = \frac{363}{1412} = 0.2571, s_F = \sqrt{\frac{0.2571(0.7429)}{1412}} = 0.01163\)
The distribution of differences has mean and standard error given by:
\(p = p_M - p_F = 0.3067 - 0.2571 = 0.0496\)
\(s = \sqrt{s_M^2 + s_F^2} = \sqrt{0.01324^2 + 0.01163^2} = 0.0176\)
What is the confidence interval?It is given by:
\(p \pm zs\)
z is the critical value, which considering that there is a 95% confidence level, it is of z = 1.96.
Then:
\(p - zs = 0.0496 - 1.96(0.0176) = 0.0151\)
\(p + zs = 0.0496 + 1.96(0.0176) = 0.0841\)
The 95% confidence interval is 0.0151 to 0.0841.
Item b:
Since 0 is not part of the confidence interval, it is not plausible that there is no difference between males and females in the proportion who agree that each person has only one true love.
More can be learned about confidence intervals at https://brainly.com/question/16162795
If A is to the right of B on a number line, which of the following must be true?
Answers
Answer:
B. a>b
Step-by-step explanation:
a is the higher number line beacuse it is farthter right than b. so a>b
Gabriela makes a profit of $0.80 for every cup of coffee that she sells at her coffee shop. She wanted to make a profit of at least $75 today on coffee. If she sold 90 cups today, which statement is correct? She met her goal, because she made less than $75 on coffee today. She met her goal, because she made more than $75 on coffee today. She missed her goal, because she made less than $75 on coffee today. She missed her goal, because she made more than $75 on coffee today.What is the value of the expression below?
(9.5 minus 3 times 1 and one-half) divided by 0.5
0.5
5
10
19.5
Answers
Answer:
She missed her goal, because she made less than $75 on coffee today.
10
Step-by-step explanation:
Target profit = $75
Profit per cup = $0.80
Number of cups sold = 90
Profit made today = Profit per cup * Number of cups sold
= $0.80 * 90
= $72
She missed her goal, because she made less than $75 on coffee today.
2. (9.5 minus 3 times 1 and one-half) divided by 0.5
(9.5 - 3 * 1 1/2) ÷ 0.5
= 9.5 - 3 * 3/2 ÷ 0.5
= 9.5 - 9/2 ÷ 0.5
= (9.5 - 4.5) ÷ 0.5
= 5 ÷ 0.5
= 10
Find the unit rate (constant of proportionality) of the distance traveled.
Number of hours
0.25 1.5 2.5 3
Distance traveled (km) 3 18 30 36
Answers
Answer:
12.
Step-by-step explanation:
if to re-write the given condition, then
\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)
it is clear, the required constant is 12 (12 per hour).
One minus five sixths equals
Answers
Hhshehehhehehehehehehehehehehehehehehehehehej
The bar graph shows how many singles were sold in the US during four consecutive years. However, the way the graph has been drawn can make it somewhat misleading. What about the graph is MOST potentially misleading?
A) The scale of years.
B) The vertical scale.
C) The sizes of the bars.
D) The colors of the bars.
Answers
PLEASE HELP!! I keep getting bots or trolls
How can you restrict the domain of the function f(x) = |x + 4| − 2 so the range of the inverse function, f -1(x), is [-4, ∞)?
A.
x ≥ 4
B.
x ≥ -4
C.
x ≥ 0
D.
x < 4
E.
x ≥ -2
Answers
Answer:
a
Step-by-step explanation:
choose number between 49-95 that is a multiple of 2,4, and 5
Answers
I got this answer wrong on my test could someone walk me through this?
Answers
Answer:
1. neither. the slopes are not negative reciprocals of each other, or are they equal.
2. perpendicular. the slopes are negative reciprocals of each other.
Step-by-step explanation:
you're welcome
solve for c.express your answer as a proper or improper fraction in simplest terms.
-7/3=2/3c-5/8
Answers
Answer:
c = -41/16
Step-by-step explanation:
You want to solve the 2-step linear equation -7/3=2/3c-5/8.
As isThe two steps for such an equation are ...
Step 1 - add the opposite of the constant on the side with the variable term.
-7/3 +5/8 = 2/3c -5/8 +5/8
-41/24 = 2/3c . . . . . . . . . . . . . simplify
Step 2 - multiply by the inverse of the coefficient of the variable.
(-41/24)(3/2) = (2/3c)(3/2)
-41/16 = c
Eliminate fractions first
Some folks like to solve equations like this by eliminating fractions as a first step. Here, that can be accomplished by multiplying the equation by 24 (the least common denominator).
(-7/3)(24) = (2/3c)(24) -(5/8)(24) . . . multiply the equation by 24
-56 = 16c -15 . . . . . . . simplify; fractions are gone
-41 = 16c . . . . . . . . . step 1, add the opposite of the unwanted constant
-41/16 = c . . . . . . . . step 2, divide by the coefficient of the variable
you want to make a scale model of a sailboat that is 51 ft long and 15 ft wide you plan to make the sailboat 17 in long how wide should the model be?
Answers
Answer:
5 in
Step-by-step explanation:
Please answer, will give 5 star.
Answers
Answer:
The first one
Step-by-step explanation:
She cant buy anything over $15, but she can buy something thats $15 :))
what is 6+6 pls help :)
Answers
Answer:
its 12 sweety hope this helps
(2/3a - 5) - (1/3a + 3) simplify
Answers
Answer:
i have no idea mate
Hey there!
(2/3a - 5) - (1/3a + 3)
= 2/3a - 5 - 1/3a + 3
COMBINE the LIKE TERMS
= (2/3a - 1/3a) - ( -5 + 3)
= 1/3a - 2
Therefore, your answer should be: 1/3a - 2
OR
Based on historical data, your manager believes that 28% of the company's orders come from first-time customers. A random sample of 157 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.24 and 0.49? help please
Answers
The probability that the sample proportion is between 0.24 and 0.49 is 0.86807.
The standard score is the number of standard deviations that a raw score deviates from or exceeds the mean of the thing being measured or observed.
The sample mean is also the population mean of 0.28.
The standard error of proportion is:
= √[( 0.28 × ( 1 - 0.28 ) / 157 ] = 0.0358
As the sample size is greater than 30, the normal distribution is used.
Z score ( 0.24 ) = ( 0.24 - 0.28 ) / 0.0358 = - 1.117
Z score ( 0.49 ) = ( 0.49 - 0.28 ) / 0.0358 = 5.86
Getting the p-value using the z table,
P( X < 0.24 ) = 0.13193
P( X < 0.49 ) = 1
So, the probability that the sample proportion is between 0.24 and 0.49 will be:
P( 0.24 < X < 0.49 ) = 1 - 0.13193 = 0.86807
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A shipping container is in the form of a right rectangular prism, with dimensions of
30 ft by 8 ft by 8 ft 9 inches. How many cubic feet of shipped goods would it hold
when it is full? Round your answer to the nearest tenth if necessary.
Answers
Answer:2,160ft
Step-by-step explanation: Volume=length * width * height
30x8x9=2160
The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
Answers
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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15). The density of mercury is 13.6 g/mL.what is the mass of 8.20 mL of mercury? 11.529b. what volume would 120 grams of mercury occupy?a.
Answers
Recall the following:
\(\text{Density}=\frac{\text{Mass}}{\text{Volume}}\text{.}\)Solving the above equation for Mass and Volume, we get:
\(\begin{gathered} Volume=\frac{\text{Mass}}{\text{Density}}, \\ \text{Mass}=\text{Density}\cdot\text{Volume.} \end{gathered}\)Therefore, if Density= 13.6 g/mL, and Volume=8.20 mL, then
\(\text{Mass}=13.6\times8.20\text{ g = 111.52 g.}\)If Mass=120 g, then:
\(\text{Volume}=\frac{120}{13.6}\text{ mL}\approx8.82\text{ mL.}\)Answer:
a) 111.52 g.
b) 8.82 mL.
Which is greater 0.652 or 0.647
Answers
Answer: 0.652 is greater by 5 thousandths.
Step-by-step explanation: 0.652 - 0.647 = 0.005
Solve the equation 4+4|2x−1|=12.
Answers
4+8x=16
8x=12
X=1.5
Select the letter for the correct answer
,
Answers
Answer:
a) 2
Step-by-step explanation:
4:8 and 6:12
4/8 and 6/12
we flip them since we want to find the conversino
8/4 and 12/6
simpilify
2 and 2
scale factor was 2
hope this helps, lmk if it is correct
It is a because 8/4 = 2 and 12/6 also = 2
Which of the following expressions is a factor of the polynomial x2+3/2x-1?
x-1
x-1/2
X-2
x+3/2
Answers
Answer:
the answer is x-1/2
