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if an aircraft is present in a certain area, a radar generates an alarm signal with...

if an aircraft is present in a certain area, a radar generates an alarm signal with probability 0.99. if an aircraft is not present, the radar generates an alarm with probability 0.1. Assume that an aircraft is present with probability 0.5.

a) what is the probability an aircraft is present and there is no alarm?

b) what is the probability that an aircraft is present, given that an alarm was signalled?
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