What is the right choice

Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court

Ksju [112]

Answer:

$(a)\dfrac{92}{117}$

$(b)\dfrac{8}{39}$

$(c)\dfrac{25}{117}$

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

$P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}$

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed) $=P(MW)+P(WM)$

$=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}$

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.
Two women are appointed

P(at least one woman is appointed) $=P(MW)+P(WM)+P(WW)$

$P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}$

In Part B, $P(MW)+P(WM)=\frac{8}{39}$

Therefore:

$P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}$

5 0

3 years ago

Neeeeeed the help please

lions [1.4K]

The correct answer is -5/7. Hope this helps.

8 0

3 years ago

How many non-congruent triangles can be formed by connecting 3 of the vertices of the cube?

alexira [117]

Answer:

The number of non-congruent triangles that can be formed by connecting 3 of the vertices of the cube is 3 non-congruent triangles

Step-by-step explanation:

From the three dimensional shape of a cube, triangles can be constructed from;

1) 6 side faces

2) 4 front face to opposite vertices triangles

3) 4 rear face to opposite vertices triangles

Each face can produce ₄C₃ = 4 triangles

Therefore;

The total number of triangles that can be formed = 4 × 6 + 4 × 4 + 4 × 4 = 56 triangles

Of the 56 triangles, it will be found that all 24 triangles from the different 6 direct faces will have the same dimension of 1, 1, √2 are congruent

The 24 triangles formed by the sides of the faces and an adjacent diagonal have the same dimension of 1, √2, √3 and are congruent

The 8 triangles formed by joining the three diagonals have the same dimension of √2, √2, √2 are congruent

Therefore, the 56 triangles comprises of a combination of three non-congruent triangle.

There are only 3 observed non congruent triangles formed by connecting three of the vertices of the cube.

3 0

3 years ago

Read 2 more answers

How many terms are there in the expression 2x - 5y + 3 + x?

swat32

Hi there, it's really not 4 terms it actually 3 terms, I will explain why. If you combine the 2x with the x that would give you 3 terms, not 4 terms. So, there are 3 terms in it, you have to make sure to simplify it.

6 0

3 years ago

Read 2 more answers

Quais são os números primos

Lynna [10]

Prime numbers are numbers that can only be divided by 1 and itself (like 3,5,7)

6 0

3 years ago