Doctors Have Devised A Test For Koronavirus That Has The Following Property GMAT Problem-Solving

This is a problem-solving question for the GMAT. In order to provide an answer, the data provided in the questions must be analyzed. The technique may involve elements from other branches of mathematics. The way the options are presented is fairly close to the right response, therefore, guessing can normally can result in errors. The question must be fully understood by the students, and they must approach the answer in the correct way.

Let's sketch the potential outcomes of this situation.
Patient having covid = Prob (0.9)
Given that the patient has covid, Prob (test being positive) = 0.9, while Prob (patient not having covid) = 0.1
Considering that the patient has covid, (Prob test being negative) = 0.1
Given that the patient does not have covid, the probability of the test being negative is equal to 0.8 The probability of the test being positive is equal to 0.2
We are now informed that the test is positive. There are two possible outcomes for this: either the patient has covid and the test is positive, or the patient does not have covid and the test is positive.

The probability of a positive test result is equal to 0.27 when divided by 0.27.
Currently, we are not being asked for the likelihood that a test will be positive.
When a patient tests positive for COVID, we are asked what the likelihood is that the patient has covid. Thus, the patient's test results are already positive.
The set of universal outcomes are therefore included in this 0.27. Or, the denominator contains this 0.27.

Which subset of this 0.27 contained the possibility that the patient actually has covid?

The main question is this. The likelihood is 0.09, or 0.1 x 0.9, in this case. Therefore, the necessary probability is 1/3 or 0.09/0.27.
Therefore, there is a 1 in 3 likelihood that a patient who tests positive has covid. This is the main justification for using medical test results with caution.

C is the correct answer.

This is a problem-solving question for the GMAT. In order to provide an answer, the data provided in the questions must be analyzed. The technique may involve elements from other branches of mathematics. The way the options are presented is fairly close to the right response, therefore, guessing can normally can result in errors. The question must be fully understood by the students, and they must approach the answer in the correct way.

Chance that a patient has covid = 0.9%
The chance that a person doesn't have covid = 0.1
Since the patient has covid, the chance that the test will be positive is 0.9.
Since the patient does not have covid, the chance that the test will come back negative is 0.8.
Since the patient does not have covid, the chance that the test will be positive is only 0.2.

Chance that the test will be positive = 0.90 0.10 + 0.90 0.20 = 0.27.

Now, no one has asked us how likely it is that the test will be good. If a patient tests positive for covid, we are asked to figure out how likely it is that he or she has covid. So the patient has already been found to have the disease. So, the set of universal results is part of this 0.27. Or, this 0.27 is in the "number of things" part.

Which part of this 0.27 was the case where the patient really does have covid?

This chance is 0.1 times 0.9, which equals 0.09. So, the needed chance is 0.09/0.27 = 1/3
So, a patient with a positive test has a one-in-three chance of having covid. This is the most important reason why we need to be careful with the results of medical tests.

The correct response is C.

This is a problem-solving question for the GMAT. Here, in order to provide an answer, the data provided in the questions must be analysed. The technique may involve elements from other branches of mathematics. The way the options are presented is fairly near to the right response, therefore guessing normally can result in errors. The question must be fully understood by the students, and they must approach the answer in the correct way.
To find the probability that a person actually has korona given that they received a positive test result, we can use Bayes' theorem. Let's define the events:

A: Person has korona
B: Test result is positive (i.e., the test says they have korona)

We are given the following probabilities:

P(A) = Probability that a person has korona = 10% = 0.10
P(B|A) = Probability of a positive test result given the person has korona = 90% = 0.90
P(~A) = Probability that a person does not have korona = 90% = 0.90
P(B|~A) = Probability of a positive test result given the person does not have korona = 20% = 0.20 (since 80% chance of a negative test result)

Now, we want to find P(A|B) - the probability that a person has korona given that they received a positive test result. According to Bayes' theorem:

P(A|B) = [P(B|A) * P(A)] / P(B)

To find P(B), the probability of a positive test result, we can use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)

Substitute the given values:

P(B) = (0.90 * 0.10) + (0.20 * 0.90)
P(B) = 0.09 + 0.18
P(B) = 0.27

Now, calculate P(A|B):

P(A|B) = (0.90 * 0.10) / 0.27
P(A|B) = 0.09 / 0.27
P(A|B) = 1/3

The probability that a person actually has korona given that they received a positive test result (P(A|B)) is 1/3.
The appropriate answer is C