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Bingel [31]
2 years ago
15

Consider a situation in which p(x) = and p(y) = . if p(x and y) is = , which best describes the events? they are independent bec

ause p(x) · p(y) = p(x and y). they are independent because p(x) p(y) = p(x and y). they are dependent because p(x) · p(y) = p(x and y). they are dependent because p(x) p(y) = p(x and y).
Mathematics
1 answer:
jeka942 years ago
4 0

Considering the given probabilities, it is found that the correct option about whether the events are independent is given as follows:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

<h3>What are independent events?</h3>

Two events, A and B are independent, if:

P(A \cap B) = P(A)P(B)

Researching this problem on the internet, the probabilities are given as follows:

P(X) = \frac{4}{5}, P(Y) = \frac{1}{4}, P(X \cap Y) = \frac{1}{5}

Hence:

P(X)P(Y) = \frac{4}{5} \times \frac{1}{4} = \frac{1}{5} = P(X \cap Y)

Hence the events are independent and the correct option is given by:

p(x) · p(y) = p(x and y). They are independent because p(x) p(y) = p(x and y).

More can be learned about probabilities at brainly.com/question/14398287

#SPJ4

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A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian
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Answer:

Question 1:

(b) 4,445

Question 2:

(c) 2.1%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Question 1:

We have no previous estimate for the population proportion, so we use \pi = 0.5.

The sample size is n for which M = 0.015. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.015 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.015\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.015}

(\sqrt{n})^2 = (\frac{1.96*0.5}{0.015})^2

n = 4268

Samples above this value should be used, and the smaller sample above this value is of 4445, so the answer is given by option b.

Question 2:

Now we find M for which n = 2222.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

M = 1.96\sqrt{\frac{0.5*0.5}{2222}}

M = 0.021

So 2.1%, and the correct answer is given by option c.

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