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Gnoma [55]
4 years ago
7

A new test to detect tb has been designed. it is estimated that 89% of people taking this test have the disease. the test detect

s the disease in 97% of those who have the disease. the test does not detect the disease in 99% of those who do not have the disease. if a person taking the test is chosen at random, what is the probability of the test indicating that the person does not have the disease?
Health
2 answers:
GaryK [48]4 years ago
5 0
The probability is 1 in 945 million
aleksley [76]4 years ago
5 0

Answer:

0.1356

Explanation:

This is a probability exercise. Let's define some probability concepts.

Given two events A and B :

(A∩B) = (A,B)

(A,B) is the intersection event where A and B occur both at the same time.

We define P(A/B) as the conditional probability '' The probability of the event A given that we know that the event B occurred'' as :

P(A/B)=\frac{P(A,B)}{P(B)}

Where P(B)>0

Now, if A is an event and A' is its complement ⇒

P(A)=1-P(A')

Finally we define the probability of the union between two events A and B :

P(A∪B) = P(A) + P(B) - P(A,B)

If the events A and B are independent between them ⇒ P(A,B) = 0 ⇒

P(A∪B) = P(A) + P(B)

Let's define the following events for this exercise :

D : ''People taking this test that have the disease''

P(D)=0.89

P(D')=1-P(D)=1-0.89=0.11

P(D')=0.11

P : ''The test is positive''

P(P/D)=0.97

P(P'/D)=1-P(P/D)=1-0.97=0.03

P(P'/D)=0.03

And P(P'/D')=0.99

We are looking the probability of P(P')

P(P') = P [(P'∩D) ∪ (P'∩D')]

Given that this events are independent between them :

P(P')=P(P',D)+P(P',D') (I)

Let's write the conditionals for this problem :

P(P'/D)=\frac{P(P',D)}{P(D)} ⇒

P(P',D)=P(P'/D).P(D)

P(P',D)=(0.03).(0.89) (II)

And the another conditional :

P(P'/D')=\frac{P(P',D')}{P(D')} ⇒

P(P',D')=P(P'/D').P(D')

P(P',D')=(0.99).(0.11) (III)

Replacing (II) and (III) in (I) :

P(P')=(0.03).(0.89)+(0.99).(0.11)

P(P')=0.1356

We find that the probability of the test indicating that the person does not have the disease ( P(P') ) is 0.1356

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Answer:

Too Many People Drink

Advocates of marijuana legalization often point to a 2015 Pew Research report that indicated that almost half of all Americans — 49 percent — had tried marijuana. That's roughly the same as the number of Americans age 12 or older who report that they currently drink alcohol. Realistically speaking and in either case, how can you outlaw something that roughly half the population does on a regular basis?  

The Alcohol Industry Is Powerful

The Distilled Spirits Council of the United States reports that the alcoholic beverage industry contributed more than $400 billion to the U.S. economy in 2010. It employed more than 3.9 million people. That's a lot of economic muscle. Making alcohol illegal would strike a significant financial blow to the U.S. economy.  

Alcohol Is Endorsed by the Christian Tradition

Prohibitionists have historically used religious arguments to ban alcohol, but they've had to fight the Bible to do it. Alcohol production was Jesus' first miracle according to the Gospel of John, and the ceremonial drinking of wine is central to the Eucharist, the oldest and most sacred Christian ceremony. Wine is a symbol in the Christian tradition. Outlawing alcohol would affect the religious beliefs of a good portion of American citizens who are protected by a Constitution that promises freedom of religion.  

Alcohol Has an Ancient History

Archaeological evidence suggests that the fermentation of alcoholic beverages is as old as civilization, dating all the way back to ancient China, Mesopotamia, and Egypt. There was never a time in recorded human history when alcohol wasn't part of our experience. That's a lot of tradition to try to overcome.

Alcohol Is Easy to Produce

Alcohol is pretty easy to make. Fermentation is a natural process, and banning the product of natural processes is always tricky. Jailhouse "pruno" can easily be made in cells using products available to prisoners, and much safer, tastier beverages can be made cheaply at home.

As Clarence Darrow put it in his 1924 anti-Prohibition speech:

Even the drastic Volstead Act has not prevented and cannot prevent the use of alcoholic beverages. The acreage of grapes has rapidly increased since it was passed and the price gone up with the demand. The government is afraid to interfere with the farmer's cider. The fruit grower is making money. The dandelion is now the national flower. Everyone who wants alcoholic beverages is fast learning how to make them at home.

In the old days the housewife's education was not complete unless she had learned how to brew. She lost the art because it became cheaper to buy beer. She has lost the art of making bread in the same way, for she can now buy bread at the store. But she can learn to make bread again, for she has already learned to brew. It is evident that no law can now be passed to prevent her. Even should Congress pass such a law, it would be impossible to find enough Prohibition agents to enforce it, or to get the taxes to pay them.

But the best argument in favor of keeping alcohol legal was the precedent set by the Prohibition to which Darrow referred. The Prohibition failed, repealed by the 21st Amendment in 1933.

Explanation:

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