For this problem, assume that the committee contains 6 men and 9 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women

Answers

Answer 1

Answer:

0.3846 = 38.46% probability that the subcommittee consists of 2 men and 1 woman.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

To solve this question, we need to know the combinations formula and conditional probability.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?

Event A: Contains both men and woman

Event B: Consists of two men and 1 woman.

Probability of containing both men and woman:

Desired outcomes:

2 men(from a set of 6) and 1 woman(from a set of 9), or 1 men(from a set of 6) and 2 women(from a set of 9). So

[tex]D = C_{6,2}*C_{9,1} + C_{6,1}*C_{9,2} = \frac{6!}{2!4!}*\frac{9!}{1!8!} + \frac{6!}{1!5!}*\frac{9!}{2!7!} = 351[/tex]

Total outcomes:

3 people from a set of 6 + 9 = 15. So

[tex]T = \frac{15!}{3!12!} = 455[/tex]

Probability:

[tex]P(A) = \frac{D}{T} = \frac{351}{455} = 0.7714[/tex]

Intersection of events A and B:

Intersection between both men and women, and 2 men and 1 woman, is 2 man and 1 women. So

Desired outcomes:

2 men(from a set of 6) and 1 woman(from a set of 9).

[tex]D = C_{6,2}*C_{9,1} = 135[/tex]

Total outcomes:

3 people from a set of 6 + 9 = 15. So

[tex]T = \frac{15!}{3!12!} = 455[/tex]

Probability:

[tex]P(A \cap B) = \frac{D}{T} = \frac{135}{455} = 0.2967[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2967}{0.7714} = 0.3846[/tex]

0.3846 = 38.46% probability that the subcommittee consists of 2 men and 1 woman.


Related Questions

2x-7y=14

Solve for x

Answers

The answer is X=7+7y/2

2/3 X 12 for simplest form

Answers

Answer:

yufcyiciygciykgc, nbhgcv

Step-by-step explanation:

98yfgouyfuchkgcbvkhgcihdiytdiytditdytdiytdityghvhgcxdfsrtyuhkjbhcgfdxzsaewrsdxfhgyujkhjmnb cvngfjkhji

Answer:

2/3 x 12 = 8/x

8x

Suppose you asked 100 commuters how much they spend each year and obtained a mean of $167 spent on transportation and a standard deviation of $40. Using the 2 SE rule of thumb, calculate a 95% confidence interval for the mean and select the values that come closest to those that would fill the spaces in the following interpretation: we can be 95% confident that the mean amount of money spent on transportation lies between _____ and _____ .

Answers

Answer:

The correct answer is "$159 and $175".

Step-by-step explanation:

The give values are:

Mean,

= $167

Standard deviation,

[tex]\sigma[/tex] = $40

Number of commuters,

n = 100

Now,

⇒ [tex]SE=\frac{\sigma}{\sqrt{n} }[/tex]

On putting the given values, we get

⇒       [tex]=\frac{40}{\sqrt{100} }[/tex]

⇒       [tex]=\frac{40}{10}[/tex]

⇒       [tex]=4[/tex]

By using the 2 SE rule of thumb, we get

= [tex]$(167 - 2\times 4)[/tex]

= [tex]167-8[/tex]

= [tex]159[/tex] ($)

Or,

= [tex](167 + 2\times 4)[/tex]

= [tex]167+8[/tex]

= [tex]175[/tex] ($)

i.e,

$159 and $175

which expressipm is equilivant to 6x + 7 - 12 * 2 -(9 + 2) - x

Answers

Answer:

7x * 14

Step-by-step explanation:

hope this helps :)

what is the slope of the line that passes through these points shown in the table
x= -1, 0, 1, 2
y= -5, -3, -1, 1​

Answers

Answer:

m=2

Step-by-step explanation:

(0,-3) (2,1)

y2-y1 1+3. 4

x2-x1 2-0. 2

4/2= 2

If m <CGB = 79°, then what is m <DGB?​

Answers

Answer:

∠DGB = 101°

Step-by-step explanation:

Given:

∠CGB = 79°

Find:

∠DGB

Computation:

We know that CD is a straight line

So,

∠CGB + ∠DGB = 180

79 + ∠DGB = 180

∠DGB = 101°

Plz help it’s due today

Answers

Answer:

4  7 /32

Step-by-step explanation:

135 : 32 = 4 ( 7)

Kết quả:  

135 /32

= 4  7 /32

Answer:

[tex]4\frac{7}{32}[/tex]

Step-by-step explanation:

Given the mixed numbers:

[tex]1\frac{1}{4}[/tex],[tex]1\frac{1}{2}[/tex],[tex]2\frac{1}{4}[/tex]

First, we need to convert them into improper fractions of the denominator of 4.

1 1/4 = 5/4

1 2/4 = 6/4

2 1/4 = 9/4

So we multiply 1 1/4 x 1 2/4 x 2 1/4 which gets us 4 7/32

help please “SHOW YOUR WORK!”

Answers

Answer:

384π cm³ ≈ 1206.37 cm³

Step-by-step explanation:

Insert the values the problem gives to us.

V = π(12)²(8)/3

⇒ π(144)(8)/3

384π ≈ 1206.37


One month Lucy rented 2 movies and video games for a total of $40. The next month she rented 5 movies and 3 video games for a total of $25. Find the
rental cost for each movie and each video game.

Answers

Answer:

the first month it was 10 each for a video game and the 2nd month it was

help me plz due today​

Answers

Answer:

4x , 2y , 5

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The terms are

4x, 2y, 5

Hope that helps

Keith has a package of 75 marbles.He gave an equal number of marbles to each of his 8 friends. How many marbles will be left over?

Answers

Answer:

9

Step-by-step explanation:

The number of marble left if Keith has a package of 75 marbles, He gave an equal number of marbles to each of his 8 friends, is 3.

What is division?

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups.

When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. For instance, 4 2 = 2. As a multiplication fact, this can be expressed as 2 + 2 = 4.

Given:

Keith has a package of 75 marbles, He gave an equal number of marbles to each of his 8 friends,

Calculate the number of marble left as shown below,

The number of marble left = Reminder of (total number of marble / 8)

The number of marble left = Reminder of(75 / 8)

The number of marble left = 3

Thus, the number of marble left is 3.

To know more about division:

https://brainly.com/question/27566440

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Please help! Marking brainliest if correct.

Answers

Answer:

110 degrees

Step-by-step explanation:

Because these angles are vertical, 5x+15=8x-42. thus, 15=3x-42, 3x=57, and x=19. 5x+15=5(19) +15=110. So, m<CDE=110 degrees.

Answer:

110°

Step-by-step explanation:

Since CDE and FDG are vertical, they are congruent, so:

5x + 15 = 8x - 42

Solve the equation for x

57 = 3x

19 = x

Then solve for one of the angles (I chose CDE but FDG would also work)

5(19)+15

95 + 15

110

A rectangular prism has a length of 6 cm, a width of 5 cm, and a depth of 4 cm. What is its volume? PL HURRY IT IS TIMED

Answers

Answer:

The answer should be 120

Step-by-step explanation: hope this helps

cual es el resuido de 729÷38​

Answers

Answer:

19

Step-by-step explanation:

NEED HELP QUICK!!
A rectangle is graphed on the coordinate grid.

On a coordinate plane, side p has points (1, 4) and (3, 6), side q has points (3, 6) and (6, 3), side r has points (4, 1) and (6, 3), and side s has points (4, 1) and (1, 4).

Which represents the equation of the side that is parallel to side s?
y = negative x + 9
y = negative x minus 3
y = x + 9
y = x minus 3

Answers

Answer:

Y = negative x + 9

Step-by-step explanation:

Find the equation of the line for side S-

m= 4-1/1-4 = 3/-3 = -1

The Gradient is -1

Since parallel lines share the same gradient, it should be either of the first two options.

We can see side Q shares the same gradient: 3-6/6-3= -1

Find the equation of the line of side Q-

y-y1= m(x-x1)

y-6= -1(x-3)

y-6=-x+3

y= -x+9

Answer:

a

Step-by-step explanation:

please help answer gets brainliest

Answers

Answer:

you got to go back to the question before that and then you will know.

Step-by-step explanation:

Geometry Help!

Please only answer if you know the answer. Look at the image below to answer the question.

Be sure to show all of your work and explain your thinking.

I posted 3 of these, so if you understand it, please go and check them out.

If you do not know the answer use the comment section, don't answer my question with a comment. Thanks, Good Luck!

Answers

Answer:

x = 8.8

Step-by-step explanation:

To solve this you need the Law of sines

sin A / a = sin B / b = sin C / c

a, b, c are the sides opposite to angles A, B and C respectively

Applied to the given triangle we have one side given, the opposite angle to be found.

sin 28 / x = sin (180 - 28 - 126) / 8.2sin 28 / x = sin 26 / 8.2x = 8.2 sin 28 / sin 26x = 8.8 (rounded)

Round to the nearest thousandth
5906÷72​

Answers

Answer:

82.028

Step-by-step explanation:

hope it helps

Solve for the coefficient a in vertex form for the parabola in Daredevil Danny’s practice jump

Answers

Answer:

-8/25  or -0.32

Step-by-step explanation:

Vertex is (25, 32)

The function in vertex form:

y = a(x - 25)² + 32

x- intercepts are 15 and 35:

0 = a(15 - 25)² + 32  or 0 = a(35 - 25)² + 320 = a*100 + 32100a = -  32a = -32/100a = -8/25  or -0.32

Which describes the shaded portion of the figure? PLEASE HELP MEEE

Answers

Answer:

1/5=20%

Step-by-step explanation:

1/2=20% is your answer

(14, 5) , (21, 3) , (26, 8) , (33, 6) , (38, 11) , ( _____ , _____ ) , ( _____ , _____ ) , (57, 12) , (62, 8) , (69, 15) , (74, 11)

fill in the sequence

Answers

Answer:

(45,9), (50, 14)

Step-by-step explanation:

the y-axis' pattern is subtract 2 and add 5.

the x-axis' pattern is add 7 then add 5.

So we get (45, 9) and (50, 14)

Deshawn bought 2 packs of markers each pack has 8 markers he gave 3 markers to ami how many markers does deshawn have left?

Answers

Answer:

13

Step-by-step explanation:

2(8)-3= 13

if my answer helped please mark as brainliest.

If the projections of vector à on x, y and z axis are 2,1,2 units respectively, find the angle at which vector à is inclined to the z-axis ​

Answers

uhh isskakia jsjajqjan

Natalie bought a three pack of erasers $1.47. At the same rate how much would a 10 pack of erasers cost?

Answers

Answer:

The price for a 10 pack of erasers would cost $4.09

Step-by-step explanation:

1.47 ÷ 3 = 0.49

0.49 × 10 = 4.9

Answer:

$4.9

Step-by-step explanation:

[ Unitary method]

3 pack of erasers = $1.47

1 pack = $1.47 / 3 = $ 0.49

10 pack = $ 0.49 x 10 = $4.9

(I hope im right!)

Write inequalities to represent the situations below.

Ryan exercises no less than 35 minutes per day. Use t to represent Ryan's amount of exercise (in minutes per day).

( ≤ < > ≥ )​

Answers

Answer:

T<45

Step-by-step explanation:

More than is a greater than symbol

Inequalities help us to compare two unequal expressions. The inequality that can be used to represent the time for which Ryan exercise is t≥35.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

Given Ryan exercises no less than 35 minutes per day. The inequality that can be used to represent the time for which Ryan exercise is t≥35.

Learn more about Inequalities:

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the difference of twelve and three times a number and negative 4

Answers

Answer:The answer is going to be 3 and this is how we came to that determination:

We are to subtract 3 times the number from 7 times the number and have it equal 12. So here is the the mathematical sentence to help us get the answer:

7X-3X=12 ; now we are going to subtract the 3 from the 7 on the left hand side of the equal sign:

4X=12 ; now we will divide each side of the equal sign by 4:

4X/4=12/4 and get X =3 ; to prove 3 is the number we are looking for, we will substitute it for X in our original sentence:

7(3)-3(3)=12

21–9=12

12=12

3 is our answer.

Step-by-step explanation:

Which figure appears to show
parallel lines?
A
B
C
D

Answers

I think the answer is C

Two gym classes are participating in Field Day. One class has 24 students and the other has 27 students. The gym teachers want to divide the students in each class into the largest possible equal groups, with no students left over. If all the groups have the same number of students, how many students are in each group?

HELP

Answers

Answer:

one class 25 and the other 26

Step-by-step explanation:

That's because if there is 24 students in each class then 3 students will be left in which the other class will take two and the other 1 student

Answer:

Step-by-step explanation:

Class 1: 24 students

Class 2: 27 students

24+27=51

51 divided by 2 = 25.5

25.5 students are in each group

State whether the triangles are similar. If so, write a similarity statement and the postulate or theorem you used. The diagram is not drawn to scale.

Answers

Givn : OK = 3, OJ = 30, KN = 1, JM = 3

ON=OK+KN=3+1=4

OM=OJ+JM=30+10=40

In triangles OKJ & ONM,

OKOJ=330=110

ONOM=440=110

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means KJNM=110 or the two sides are parallel.

Hence ˆK=ˆN,ˆJ=ˆM corresponding angles.

Two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

The similarity statement is: [tex]\triangle NOM \sim \triangle KOJ[/tex]Theorem: Side-Angle-Side Similarity Theorem (SAS)

Recall:

Two triangles can be proven to be similar by the SAS Similarity Theorem, if they both have two pairs of corresponding side lengths that are proportional to each other and also have a corresponding included angle that is congruent to each other.

Using the image given, let's determine if two of the given side lengths of each triangle are proportional to each other.

Given:

OJ = 30OM = 30 + 10 = 40OK = 3ON = 3 + 1 = 4

Thus:

[tex]\frac{OM}{OJ} = \frac{ON}{OK}[/tex]

Substitute

[tex]\frac{40}{30} = \frac{4}{3}[/tex] (proportional)

Also, <NOM and <KOJ are congruent to each other (included angles).

Therefore, since we have two sides in each triangle that are proportional to each other, and a corresponding included angle in both triangles that are congruent, both triangles are similar.

The similarity statement is: [tex]\triangle NOM \sim \triangle KOJ[/tex]

Theorem: Side-Angle-Side Similarity Theorem (SAS)

Learn more here:

https://brainly.com/question/11361067

The salaries of 4 players on a professional basketball team average $200,000 per year. If a fifth player is hired for $400,000 per year, what will be the average salary for the 5 players? Answer with supporting work:​

Answers

If salary average of 4 players is making $200,000/yr, what's the total payroll?  It should be $200K x 4 or $800,000.

Now if you add in that 5th player at $400,000 what is the total payroll of all 5 players?  It should be $800,000 + $400,000 = 1,200,000.  From there you can find the average of the 5 players by dividing!

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