SOLUTION: A person with tuberculosis is given a chest? x-ray. Four tuberculosis? x-ray specialists examine each? x-ray independently. If each specialist can detect tuberculosis 89?% of the t

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Question 1198942: A person with tuberculosis is given a chest? x-ray. Four tuberculosis? x-ray specialists examine each? x-ray independently. If each specialist can detect tuberculosis 89?% of the time when it is? present, what is the probability that at least 1 of the specialists will detect tuberculosis in this? person?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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A person with tuberculosis is given a chest? x-ray.
Four tuberculosis? x-ray specialists examine each? x-ray independently.
If each specialist can detect tuberculosis 89?% of the time when it is
present, what is the probability that at least 1 of the specialists
will detect tuberculosis in this? person?
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The solution is in two steps.


Step 1.  Then the probability that no one of 4 specialists will detect 

         tuberculosis is  %281-0.89%29%5E4 = }}}0.11^4}}} = 0.00014641   (rounded).


Step 2.  The probability under the problem's question is the COMPLEMENT to it

         P = 1 - %281-0.89%29%5E4 = 1 - 0.00014641 = 0.999853.    ANSWER

Solved.