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In: Statistics and Probability

A covid-19 test manufacturer is testing its newest instant test. It tests a total of 500...

A covid-19 test manufacturer is testing its newest instant test. It tests a total of 500 people, 100 of whom are known to be have the virus. The following table shows the results:

Have virus (V)

Do not have virus

(V’)

Total

Test is positive (T)

90

40

130

Test is negative (T’)

30

160

190

Total

120

200

320
  1. Find the probability that a person has the virus but tests negative.
  2. Find the probability that a person who has the virus tests negative.
  3. Find the probability that a person who tests negative has the virus.
  4. An acquaintance of yours has a negative test result. What is the probability that she does not have the virus?

Solutions

Expert Solution

Answer:

given Data

A covid - 19 test manufacturer is testing its newest instant test.

It tests a total of 500 people , 100 of whom are known to be have the virus.

Have virus (V) Do not have virus(V') Toatl
Test is pasitive(T) 90 40 130
Test is negative (T’) 30 160 190
Total 120 200 320

a) Find the probability that a person has the virus but tests negative.

P(Person has the virus but tests negative)

= 0.0938

b) Find the probability that a person who has the virus tests negative.

   P(Person who has the virus tests negative)

  

= 0.25

c) Find the probability that a person who tests negative has the virus .

     P(Person who tests negative has the virus)

= 0.1579

d)  An acquaintance of yours has a negative test result. What is the probability that she does not have the virus?

P(Person who does not have the virus)

= 0.8421

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