Question

Question 3: A new virus has been circulating in Townsville. Fortu- nately, a pharmaceutical company called Umbrella Inc. has developed a test for diagnosing - before symptoms appear – individuals who are infected so that they can be preemptively quarantined. The probability an individual is currently infected is . Therefore, the prob- ability he/she is not infected is . If an individual is infected, Umbrella Inc.'s test always reports “VIRUS DETECTED” (i.e. with probability 1), but if an individual is not infected the test reports "VIRUS DETECTED” with probability į and “VIRUS NOT DETECTED” with probability . Let A represent the possible infection status of an individual, so that A=1 means "the individual is infected" and A=0 means "the individual is not infected." Let B represent the possible results of Umbrella Inc.'s test, so B = 1 means “VIRUS DETECTED” and B=0 means “VIRUS NOT DETECTED." Use the information above and use properties of joint and conditional prob- abilities to compute: (a) P(A= 1) (b) P(A=0) (c) P(B = 1A = 1)

Answer 1

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