1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lesechka [4]
3 years ago
12

Five men and 5 women are ranked according to their scores on an examination. Assume that no two scores are alike and all 10! pos

sible rankings are equally likely. Let X denote the highest ranking achieved by a woman. (For instance, X = 1 if the top-ranked person is female.) Find P { X = i } , i = 1 , 2 , 3 , … , 8 , 9 , 10 .
Mathematics
1 answer:
m_a_m_a [10]3 years ago
3 0

Answer:

P(X=1)=\frac{1}{2}\\P(X=2)=\frac{5}{18}\\P(X=3)=\frac{5}{36}\\P(X=4)=\frac{5}{84}\\P(X=5)=\frac{5}{252}\\P(X=6)=\frac{1}{252} \\P(X>6)=0

Step-by-step explanation:

Let's define the following event :

X : ''Highest ranking achieved by a woman''

There are five men and five women so the lowest ranking possible is 6, this means that all five men achieved a better ranking than all five women.

In terms of the variable :

X can assume the following values :

X=1\\X=2\\X=3\\X=4\\X=5\\X=6

⇒ P(X=7)=0\\P(X=8)=0\\P(X=9)=0\\P(X=10)=0

⇒ P(X>6)=0

Now let's calculate the probability function for X

P(X=1)=\frac{(5)(9!)}{(10!)}=0.5=\frac{1}{2}

We write on the denominator the total ways to arrange ten different persons in a line. This number is 10!

On the numerator we write the total cases in which the first person is a woman ⇒ (5).(9!)

Because they are five different women and when you pick one of then they are 9! ways to arrange the 9 remaining persons

Following this logic, we continue calculating the probability function :

P(X=2)=\frac{(5)(5)(8!)}{(10!)}=\frac{5}{18}

Again : Five different ways to choose between the five men in the first position.Then, 5 different ways to choose between the five women.And finally, 8! ways to arrange the remaining persons

P(X=3)=\frac{(5)(4)(5)(7!)}{(10!)}=\frac{5}{36}

Here we have : five different ways to choose between five men.Four different ways to choose between the four remaining men.Five different ways to choose between the five women for the third position and finally 7! ways to arrange the remaining persons.

P(X=4)=\frac{(5)(4)(3)(5)(6!)}{(10!)}=\frac{5}{84}

P(X=5)=\frac{(5)(4)(3)(2)(5)(5!)}{(10!)}=\frac{5}{252}

P(X=6)=\frac{(5)(4)(3)(2)(1)(5)(4!)}{(10!)}=\frac{1}{252}

You might be interested in
If angle y measures 65 degrees how much does x measure?
belka [17]

Answer:

supplementary angles add up to 180°

given y=65° thus...

x+y=180°

x + 65°=180°

x=180°- 65°

x=115°

8 0
3 years ago
Read 2 more answers
Please helllppp will give lots of points!!!!
kondaur [170]

Answer:

1. start is 1/3

2. is 1/3

3. is 1 out of 2

4. is 1 out of 6

5. is 2 out of 3

6. is 1 out of 2

7. is 5 out of 6

8. is 1 out of 6

then finished!!!

I hope this helped

7 0
3 years ago
The total surface area of this cuboid is 112^2
Nastasia [14]

The value of x is 3

<h3>How to solve for x?</h3>

The given parameters are:

Length = 10cm

width = 2cm

Height = x

The surface area is calculated as;

Area = 2 *(lw + lh + wh)

So, we have:

2 * (10 * 2 + 2x + 10x) = 112

Evaluate the like terms and divide by 2

20 + 12x = 56

Subtract 20 from both sides

12x = 36

Divide by 12

x = 3

hence, the value of x is 3

Read more about surface areas at:

brainly.com/question/2835293

#SPJ1

7 0
2 years ago
05.06)Which of the following best describes interval C on the graph shown?
Korolek [52]
Linear decreasing

I haven't learned this is class yet, but I had a bf that taught me this
8 0
3 years ago
Read 2 more answers
Every month Marina pays $79 for mobile phone service, $59.95 for cable service, and $45.50 for internet service. She can switch
belka [17]
She would save 54.45 because addding them up individually before the plan would cost 184.49 and to find the difference all you have to do is subtract 184.49-129.99 and that would tell you how much she saved
6 0
3 years ago
Read 2 more answers
Other questions:
  • Directions: Drag each tile to the correct box.
    6·2 answers
  • Subtract negative 24 from 11.
    13·2 answers
  • which list shows the numbers in order from least to greatest? a. 5.4 × 104, 5.4 × 103, 4.5 × 104 b. 5.4 × 103, 5.4 × 104, 4.5 ×
    15·1 answer
  • To meet the copper requirements of a growing pain, the feed must contain 4 mg copper per kilogram of dry matter of feed. If a pi
    5·1 answer
  • How is 6.35 x 10^11 written in standard form
    10·1 answer
  • D(x, y) = (3x, 3y)
    13·1 answer
  • Tell whether the ratios form a proportion.<br><br> 1 to 3 and 7 to 21
    5·1 answer
  • If Jim works at Fire Fighting Equipment, has $32,874 in sales in one week, and as paid a weekly salary of $452 plus a commission
    6·1 answer
  • 8. Solve for x. Round to the nearest hundredth If necessary.
    10·1 answer
  • How tall will be the entire arrangement in standard ratio?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!