Question

Assume that 1% of students returning from South Korea and Japan are infected with the virus. Their saliva test accuracy is 99%. Suppose a particular student’s saliva test is negative. An unprofessional person explains the following -> First, the probability of the student being infected by the virus is 0.01 (i.e, 1%). Since an independent test showed that he was not infected, the error probability is 0.01, ie (i.e 1%). The actual probability that a student is infected is 0.01 × 0.01 = 0.01%. Comment on his interpretation.

Answer 1

Let there be 1000 students returning from South korea and Japan.

1% of the students are infected

Total No of inffected students is 10

Probability of a student being infected is 10/1000= 0.01

Since, their saliva test accuracy is 99% that is if 100 students with the virus is tested it will only give positive result for 99 students.

The error probability is 1/100= 0.01

The actual probability that a student is infected is 0.01 * 0.01 = 0.0001 = 0.01%

The interpretation is correct.