A fair coin is flipped 3 times. It lands facing heads up 2 out of 3 times.

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

The team won 5 out of 8 games if the team played 32 games how many did they win

Rus_ich [418]

Answer:

20

Step-by-step explanation:

32/8 = 4

4 x 5 = 20

:)

7 0

3 years ago

Someone please help me!!

Phoenix [80]

Answer:

x=6

UV=40

WV=40

UW=30

Step-by-step explanation:

GIVEN UV=WV

6X+4=40

X=6

NOW PUT X=6 in WV AND UW

6 0

3 years ago

The water tank in the diagram is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its hei

Angelina_Jolie [31]

Answer:

6433.98 ft

Step-by-step explanation:

In order to find what 25% of the tank's capacity is, we know to know the full capacity of the tank then take 25% of that. The volume formula for a right circular cone is

$V=\frac{1}{3}\pi r^2h$