What is 49/16 simplified

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

m_a_m_a [10]

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.

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

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

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

3 0

3 years ago

Suppose you just purchased a digital music player and have put 15 tracks on it. After listening to them you decide that you like

Lilit [14]

The given case is an example of permutation problem because the order is important given that you should like the first two songs. The sample space is calculated through the equation,
15P2 = 210
Then, there are 3 songs that you liked, the probability of picking 2 out of them is,
3P2 = 6
Dividing the latter by the earlier result will give us an answer of 1/35.

8 0

3 years ago

There are "n" delicious sweets in the bag. You know that 6 of them are orange and the rest are yellow. Hannah takes a random swe

nikitadnepr [17]

At the point when Hannah takes her first sweet from the sack, there is a 6/n chance it is orange.
This is because that there are 6 orange desserts and n desserts altogether.
When Hannah takes out her second sweet, there is a 5/(n-1) chance that it is orange.
This is because there are just 5 orange desserts let alone for an aggregate of n-1 desserts.
The possibility of getting two orange desserts in succession is the main likelihood increased by the second one: 6/n x 5/n–1
The question lets us know that the shot of Hannah getting two orange desserts is 1/3.
So: 6/n x 5/n–1 = 1/3
Now, rearrange this problem.
(6x5)/n(n-1) = 1/3
This gets to be:
30/(n² – n) = 1/3
Times by 3 on both sides:
90/(n² – n) = 1
What's more, doing likewise with (n² – n):
So (n² – n) = 90
Our answer is: n² – n – 90 = 0

3 0

3 years ago

What expression is the simplified form of “-12+5a-a-6a+8a+8+3a”? Please explain your reasoning.

kramer

Combine like terms:

-12 + 5a - a - 6a + 8a + 8 + 3a

$-12 + 5a - a - 6a + 8a + 8 + 3a$

5a - a = 4a

4a - 6a = -2a

-2a + 8a = 6a

6a + 3a = 9a

-12 + 8 = -4

Answer

$9a - 4$

4 0

4 years ago

Read 2 more answers

What value of x would make the figure below a parallelogram? please show your work!

lara31 [8.8K]

Answer:

x = 8

Step-by-step explanation:

Since the sum of all angles of a parallelogram is equal to 360 degrees, <Z + <Y is half of the parallelogram, and therefore <Z + <Y = 180 degrees.

16x-4 + 7x = 180, combine like terms

23x - 4 = 180, add 4 on both sides (isolate variable)

23x = 184, divide 23 on both sides

x = 8

8 0

2 years ago