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3 years ago

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What is the difference? startfraction x over x squared 3 x 2 endfraction minus startfraction 1 over (x 2) (x 1) endfraction star

tfraction x minus 1 over 6 x 4 endfraction startfraction negative 1 over 4 x 2 endfraction startfraction 1 over x 2 endfraction startfraction x minus 1 over x squared 3 x 2 endfraction

1 answer:

emmainna [20.7K]3 years ago

8 0

Answer:

choose D

Step-by-step explanation:

x/(x²+3x+2) - 1/[(x+2)(x+1)]

x² + 3x + 2 = x² + 2x + x + 2

= x(x + 2) + (x + 2)

= (x + 2)(x + 1)

= x/[(x+2)(x+1)] - 1/[(x+2)(x+1)]

= (x-1)/[(x+2)(x+1)]

= (x-1)/(x²+3x+2)

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The probability that a person is sick is: 0.008
The probability that a test is positive, given that the person is sick is 0.9833
The probability that a test is negative, given that the person is not sick is: 0.9899
The probability that a person is sick, given that the test is positive is: 0.4403
The probability that a person is not sick, given that the test is negative is: 0.9998
A 99% accurate test is a correct test

<u />

<u>(a) Probability that a person is sick</u>

From the table, we have:

$\mathbf{Sick = 59+1 = 60}$

So, the probability that a person is sick is:

$\mathbf{Pr = \frac{Sick}{Total}}$

This gives

$\mathbf{Pr = \frac{60}{7500}}$

$\mathbf{Pr = 0.008}$

The probability that a person is sick is: 0.008

<u>(b) Probability that a test is positive, given that the person is sick</u>

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

So, the probability that a test is positive, given that the person is sick is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}$

This gives

$\mathbf{Pr = \frac{59}{60}}$

$\mathbf{Pr = 0.9833}$

The probability that a test is positive, given that the person is sick is 0.9833

<u>(c) Probability that a test is negative, given that the person is not sick</u>

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Not\ Sick = 75 + 7365 = 7440}$

So, the probability that a test is negative, given that the person is not sick is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}$

This gives

$\mathbf{Pr = \frac{7365}{7440}}$

$\mathbf{Pr = 0.9899}$

The probability that a test is negative, given that the person is not sick is: 0.9899

<u>(d) Probability that a person is sick, given that the test is positive</u>

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

$\mathbf{Positive=59 + 75 = 134}$

So, the probability that a person is sick, given that the test is positive is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}$

This gives

$\mathbf{Pr = \frac{59}{134}}$

$\mathbf{Pr = 0.4403}$

The probability that a person is sick, given that the test is positive is: 0.4403

<u>(e) Probability that a person is not sick, given that the test is negative</u>

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Negative = 1+ 7365 = 7366}$

So, the probability that a person is not sick, given that the test is negative is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}$

This gives

$\mathbf{Pr = \frac{7365}{7366}}$

$\mathbf{Pr = 0.9998}$

The probability that a person is not sick, given that the test is negative is: 0.9998

<u>(f) When a test is 99% accurate</u>

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.

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