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Probability Question And Answer

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Probability
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George Washington University
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Probability Question and Answer
Question 1: SCENARIO
In the wake of the global Corona Virus pandemic, a researcher in the province of Wuhan in
China conducted a survey in order to determine the chances of showing the initial signs
and symptoms of the virus and testing positive for the virus. The researcher surveyed a
total of 10000 Chinese people in a village in Wuhan and observed that 200 among them did
show initial signs of the virus and upon testing, only two did not have the Corona virus. On
the other hand, 882 people of those who had no initial signs gave positive results upon
being tested.
Question 2: TREE DIAGRAM
Q: Using the researcher’s findings, represent the scenario using a tree diagram.
Solution
From the scenario, the following probabilities are found as follows:
If shown initial Corona Signs, then:













If not shown initial Corona Signs, then:
















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Therefore, the resulting tree diagram is shown below:
Question 3: Conditional Probability
Q: Find the probability that one shows signs of the Corona virus given that he/she tested
positive to the virus using the Conditional probability via the law of total probability.
Solution
The probability that one shows signs given that he/she tests positive to the Corona virus is
given by conditional probability via the law of total probability as follows:
But, the law of total probability gives (from Q4):

Therefore,
  


Question 4: Law of Total Probability
Q: Using the researcher’s findings, find the probability that one tests positive for the
Corona virus (using the law of total probability).
Solution
The probability that one tests positive  for the Corona virus is given by the law of total
probability as follows:
  
 
  
From the tree diagram above:
  
   

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Last Name 1 Name Instructor's name Course Date Probability Question and Answer Question 1: SCENARIO In the wake of the global Corona Virus pandemic, a researcher in the province of Wuhan in China conducted a survey in order to determine the chances of showing the initial signs and symptoms of the virus and testing positive for the virus. The researcher surveyed a total of 10000 Chinese people in a village in Wuhan and observed that 200 among them did show initial signs of the virus and upon testing, only two did not have the Corona virus. On the other hand, 882 people of those who had no initial signs gave positive results upon being tested. Question 2: TREE DIAGRAM Q: Using the researcher’s findings, represent the scenario using a tree diagram. Solution From the scenario, the following probabilities are found as follows: If shown initial Corona Signs, then: 200 = 0.02 10000 198 𝑃? ...
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