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3 years ago

5

The probability of event A is x, and the probability of event B is y. If the two events are independent, which of these conditio

ns must be true?

1 answer:

Inga [223]3 years ago

5 0

Answer:

P(B|A)=y

Step-by-step explanation:

The complete question is shown in the attachment.

If the events, A and B are independent, then

P(A and B) = P(A)×P(B)

But from the question:

P(A)=x and P(B)=y

This implies that:

P(A and B) = xy

Also, the conditional probabilities are:

P(A\B)=P(A)=x

P(B\A)=P(B)=y

Therefore the correct answer is A

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Question 1. If the perimeter of Rectangle ABCD is 34y+2. What is the width?

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Answer:

Question 1. If the perimeter of Rectangle ABCD is 34y+2. What is the width?

Question 2. What is the area of Rectangle ABCD in terms of y?

Question 3. If the perimeter of the rectangle is 70. What is it’s area?

Question 4. What are the length and width of the rectangle?

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3 years ago

Lindsey Wilson was the top scorer in a women's professional basketball league for the 2006 regular season, with a total of 814 p

baherus [9]

Answer:

The number of free throws, two-point throw, and three-point throw are 135, 173, and 111 respectively.

Step-by-step explanation:

Let x,y, and z are the numbers of two-point field goals, numbers of three-point field goals, and the number of free-throws (one-point goal) respectively.

The total points= 814

$\Rightarrow 2x+3y+z=814\;\cdots(i)$

As the number of two-point goals was 49 less than double the number of three-point field goals she made.

$\Rightarrow x=2y-49 \;\cdots(ii)$

Again, the number of free goals was 38 less than the number of two-point field goals she made.

$\Rightarrow z=x-38\;\cdots(iii)$

From equations (i) and (iii)

2x+3y+x-38=814

$\Rightarrow 3x+3y=852$

$\Rightarrow x+y=284$

$\Rightarrow 2y-49+y=284$ [using equation (ii)]

$\Rightarrow 3y=333$

$\Rightarrow y=111$

From equation (ii),

$x= 2\times111-38=173$

From equation (iii),

$z=173-38=135$ .

Hence,

The number of free throws, z= 135

The number of two-point throw, x=173

The number of three-point throw, y=111.

3 0

3 years ago

A certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder. In

lord [1]

Answer:

95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

Step-by-step explanation:

We are given that a certain geneticist is interested in the proportion of males and females in the population who have a minor blood disorder.

A random sample of 1000 males, 250 are found to be afflicted, whereas 275 of 1000 females tested appear to have the disorder.

Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;

P.Q. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of males having blood disorder= $\frac{250}{1000}$ = 0.25

$\hat p_2$ = sample proportion of females having blood disorder = $\frac{275}{1000}$ = 0.275

$n_1$ = sample of males = 1000

$n_2$ = sample of females = 1000

$p_1$ = population proportion of males having blood disorder

$p_2$ = population proportion of females having blood disorder

<em>Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.</em>

<u>So, 95% confidence interval for the difference between the population proportions, </u><u>(</u> $p_1-p_2$ <u>)</u><u> is ;</u>

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 < $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ < ${(\hat p_1-\hat p_2)-(p_1-p_2)}$ < $1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ) = 0.95

P( $(\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ < ( $p_1-p_2$ ) < $(\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ) = 0.95

<u>95% confidence interval for</u> ( $p_1-p_2$ ) =

[ $(\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ , $(\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+ \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ]

= [ $(0.25-0.275)-1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} }$ , $(0.25-0.275)+1.96 \times {\sqrt{\frac{0.25(1-0.25)}{1000}+ \frac{0.275(1-0.275)}{1000}} }$ ]

= [-0.064 , 0.014]

Therefore, 95% confidence interval for the difference between the proportions of males and females who have the blood disorder is [-0.064 , 0.014].

8 0

3 years ago

Wendy can wash a car twice as fast as Jason. When they work together, Wendy and Jason can wash a large van in 2 hours. How many

Ugo [173]

X= number of hours would it take Jason to wash the van by himself.
2x=number of hours would it take Wendy to wash the van by herserlf.

<span>we calcaulate the fraction of work by Jason during one hour </span>

x hours-----------------------------1 work
1 hour---------------------- fraction of work during one hour.

fraction of work during one hour=(1 hour * 1work) / x hours=1/x

we calculate the fraction of work by Wendy during one hour.
2x hours-----------------------------1 work
1 hour---------------------- fraction of work during one hour.

fraction of work during one hour=(1 hour * 1work) / 2x hours=1/2x

We can suggest this equation:
2 hours(fraction of work by Jason during one hour + fraction of work by Wendy during one hour)=1 work

2(1/x + 1/2x)=1

least common multiple=2x
2(2+1)=2x
2(3)=2x
6=2x
x=6/2
x=3

answer: 3 hours would ti take Jason to wash the van by himself.

5 0

3 years ago

Which is the most likely meaning of the word anachronous? (1 point)

ad-work [718]

Answer:

Not in the right time

Step-by-step explanation:

ana is the root of before and chronous=krounus, being the Greek word for time.

6 0

2 years ago