Question

Q3: Flu shots are provided by student health center at UCSD. In the current season, the percentage of flu infection in the student population is 10%. For those who received a flu shot, the percentage reduces to 1%, 50% of the students on campus receive the flu shot. 1. What is the probability of flu infection if a student has not received a flu shot? 2. If a student is not infected by the flu, what is the probability that the student has received a flu shot? 3. The student health center introduces a detection kit to campus. If the kit indicates a positive result, there is 0.95 probability of flu infection. If the kit indicates a negative result, there is no infection. The flu shot does not influence the detection results. What is the probability that a student receives a flu shot if the detection result is positive?

Answer 1

1)
probability of flu infection is 10% if a student has not received flu shot
2)
P(received a flu shot| not infected)
= P( received a flu shot and not infected)/P(not infected)
= 0.5 * ( 1 - 0.01) / (0.5 * 0.99 + 0.5 * (1 - 0.1))
= 0.52380