All categories

3 years ago

Find the sample space for a committee of two chosen from Alice (A), Bill (B), Carol (C), and David (D).

Mathematics

1 answer:

Finger [1]3 years ago

4 0

Answer:

(a) C. {(A, B), (A, C), (A, D), (B, C), (B, D), (C, D)}

(b) C. {(A,B),(A,D),(B,C),(C,D)}

Step-by-step explanation:

Given four members eligible for selection:

Alice (A), Bill (B), Carol (C), and David (D).

The possible combinations are:

(A,B),(A,C),(A,D),(B,A),(B,C),(B,D),(C,A),(C,B),(C,D), (D,A),(D,B), (D,C)

Part A

Since the same pairs are equal i.e. (A, B)=(B , A),

The Sample space for a committee of two is:

{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}

This is Option C.

Part B

If both genders must be represented, we remove the entries that contain the same gender from the sample space above.

A and C -Female

B and D - Male

{(A,B),(A,C),(A,D),(B,C),(B,D),(C,D)}

Therefore, the sample space if both genders are to be represented is:

{(A,B),(A,D),(B,C),(C,D)}

This is Option C.

You might be interested in

Fill in the blanks. The vertical line that contains the vertex is called the blank ?

zysi [14]

Answer:

Axis of symmetry

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Complete the following sentence. The slope of the graph of y = x is

Mrac [35]

Answer:

The slope of y=x is 1

Step-by-step explanation:

Slope = 1

7 0

3 years ago

Which best describes the meaning of the statement "If A, then B"? A. If A is false, then B might be false. B. If A is false, the

Lina20 [59]

In mathematics, the statement if a, then b, says that if a is true, then be is true. If you think about it, this makes sense too. That means that the answer is C., because of the definition of the statement.

8 0

3 years ago

Read 2 more answers

The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir

Paha777 [63]

Answer:

95% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean time = 5.15 years

$\sigma$ = sample standard deviation = 1.68 years

n = sample of college graduates = 4400

$\mu$ = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

level of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95