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
100 POINTS
IgorLugansk [536]

Answer:

Step-by-step explanation:

90.9^2 - 21.2^2 = b^2

8,262.81 - 449.44 = b^2

b = 88.39326897450959189749074160142

7 0
3 years ago
A paddle boat can move at a speed of 2 ​km/h in still water. The boat is paddled 16 km downstream in a river in the same time it
MaRussiya [10]
<span>going downstream - 

t = 14/(2 + v) 

going upstream - 

t = 7/(2 - v) 

14/(2 + v) = 7/(2 - v) 

(2 + v)/2 = 2 - v 

v = 2/3km/h</span><span>
</span>
6 0
3 years ago
PLZZZZZZ I NEED HELP IM SO TIRED PLZZZZZZZZ
ipn [44]

Answer:

8.99

Step-by-step explanation:

\left|-46.09+51.64\right|+\left|18.08-21.52\right|

\left|-46.09+51.64\right|=5.55

\left|18.08-21.52\right|=3.44

5.55+3.44

8.99

8 0
2 years ago
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Bezzdna [24]
The answer is option C. 9xy sqrt 2x
5 0
3 years ago
How do you write 3 15/44 as a decimal ??
Gnesinka [82]

Answer: 3.34 or 3.34090909

Step-by-step explanation: put 15 divided by 44 in your calculator. Yous should get 0.34090909 , then put your original 3 in front of that. Round your number if that is required.

4 0
3 years ago
Other questions:
  • 10, 13, 19, 28, 40 repeating patterns
    6·1 answer
  • Solve y over negative 2 + 5 = 13.
    13·1 answer
  • Is x + 10 a factor of the function f(x) = x3 − 75x + 250? Explain.
    11·1 answer
  • F(x)= 20 + 12(x - 2)​
    14·2 answers
  • The step function f of x is graphed what is the value of f of 0?​
    6·2 answers
  • PLEASEEEEEEEE HELLLP MEEE!!! GIVING 95 POINTS!!!
    6·2 answers
  • 2) Customer number two gives you a
    14·1 answer
  • Help me please thank you
    5·1 answer
  • What is the area of the shaded region?
    13·1 answer
  • If you are told to calculate simple interest, and you are told to calculate the interest for 6 months, what would you need to do
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!