Suppose that there are two tests for Covid-19, which do not require destruction of the test

sample. Workers at a large factory each provide a sample taken from their nose. The sample

is then sent to Laboratory 1 (Lab 1) where it is tested for Covid-19, using Test 1.

It is then sent to Laboratory 2 (Lab 2) and tested for Covid-19. The two tests are based on

entirely different principles, the two laboratories are located in different cities and Lab 2 is

not informed of the results of the tests from Lab 1.

(i) Suppose that a worker has Covid-19. Suppose that 90 percent of those with Covid-19

test positive at Lab 1 and 80 percent of those with Covid-19 test positive at Lab 2.

What is the probability that the worker will test positive at both laboratories? If you

think it is not possible to fifind this probability, give a reason. If you think it is possible,

give your reasoning.

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(ii) Suppose now, that instead of the information given in Part (i) all you are told is that 90

percent of the workers test positive at Lab 1 and 80 percent of the workers test positive

at Lab 2.

What is the probability that a randomly selected worker will test positive at both

laboratories? If you think it is not possible to fifind this probability give a reason. If

you think it is possible, give your reasoning.