Question

A terrible new virus has been discovered amongst​ beef-cattle in Southern Alberta. It is estimated that 6% of all​ beef-cattle are infected with this virus. A team of veterinarians have developed a simple test. Indications are that this test will show a positive result​ - indicating the​ beef-cow being tested has the virus​ - with a probability of 0.95. Unfortunately, this test has a​ false-positive probability of 0.09.

​(a) A​ beef-cow in Southern Alberta was randomly chosen and given this test. The test results were​ positive, indicating the​ beef-cow has the virus. What is the probability that this particular​ beef-cow actually does have the​ virus?

​(b) What is the probability that a​ beef-cow that tests negative for this​ virus, actually has the​ virus?

Answer 1

a)

P(tested positive)=P(virus and tested positive)+P(not have virus and tested positive)

=0.06*0.95+(1-0.06)*0.09=0.1416

therefore probability that this particular​ beef-cow actually does have the​ virus given tested positive

=P(virus and tested positive)/P(tested positive)=0.06*0.95/0.1416=0.402542

b)

P(tested negative)=1-P(tested positive)=1-0.1416=0.8584

hence P(actually has the​ virus given tested negative)

=P(virus and tested negative)/P(tested negative)=0.06*(1-0.95)/0.8584=0.003495