Question

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Stat

(3)

One-half percent of the population has CORONA Virus. There is a test to detect CORONA. A positive test result is supposed to mean that you have CORONA but the test is not perfect. For people with CORONA, the test misses the diagnosis 2% of the times. And for the people without CORONA, the test incorrectly tells 3% of them that they have CORONA.
(i) What is the probability that a person picked at random will test positive?
(ii) What is the probability that you have CORONA given that your test comes back positive?

(4)

A device is composed of two components, A and B, subject to random failures. The components are connected in parallel and, consequently, the device is down only if both components are down. The two components are not independent. We estimate that the probability of:
a failure of component A is equal to 0.2;
a failure of component B is equal to 0.8 if component A is down;
a failure of component B is equal to 0.4 if component A is active.
(a)

Calculate the probability of a failure
(i) of component A if component B is down
(ii) of exactly one component
(b)

In order to increase the reliability of the device, a third component, C, is added in such a way that components A, B, and C are connected in parallel. The probability that component C breaks down is equal to 0.2, independently of the state (up or down) of components A and B. Given that the device is active, what is the
probability that component C is down?

Answer 1