Question

A terrible new virus has been discovered amongst​ beef-cattle in Southern Alberta. It is estimated that  

44​%

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

0.950.95.

​Unfortunately, this test has a​ false-positive probability of

0.060.06.

​(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?

​(a) If the​ beef-cow tests positive for the​ virus, the probability that this​ beef-cow actually has the virus is

nothing.

​(Enter your answer to four​ decimals)

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

nothing.

​(Enter your answer to four​ decimals)

Answer 1

(a)

From the given data, the following Table is calculated:

	Test Positive	Test Negative	Total
Infected with virus	0.04X0.95=0.038	0.04-0.038=0.002	0.04
Not infected with virus	0.96 X 0.06 = 0.0576	0.96 - 0.0576 = 0.9024	0.96
Total	0.0956	0.9044	1.00

P(Infected with virus/ Test Positive) = P(Infected with virus AND Test Positive)/ P(Test Positive)

                                                  = 0.038/ 0.0956

                                                    = 0.3975

So,

Answer is:

0.3975

(b)

P(Infected with virus/ Test Negative) = P(Infected with virus AND Test Negative)/ P(Test Negative)

                                                  = 0.002/ 0.9044

                                                    = 0.0022

So,

Answer is:

0.0022