Venn diagrams

Question

The company is conducting a survey to determine the spread of two strains of viruses (type A and type B) in a certain wing of a hospital. Out of 450 patients,
267 tested positive to virus A
253 tested positive to virus B
40 tested negative to both

Draw a Venn diagram to represent all the information above.

If one patient is chosen at random, what is the probability that the patient tested is negative to both A and B?

Find the probability that a patient chosen at random:
Tested positive to virus A only.
Tested positive to virus A given that he/she tested positive to virus B.

Answer 1

 

A = 267 People

 

B = 253 People

 

Neither = 40  

 

A ∩ B = 410  - 267 = 

 

The number of people that tested positive for virus A & B, is

       A ∩ B = A + B - (450 - 40) 

       = 267 + 253 - 410

       = 110

 

The number of people that tested positive for A only is

       267 - 110

       = 157       

 

The probability of a random patient testing positive for A only is

 

       157/450

      

The probability of a random patient testing positive for A given they tested positive for B is:

       110/253