An athlete suspected of having used steroids is given two tests that operate independently of each other. Test A has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroids have been used. What is the probability that atleast one test is positive if steroids have been used?

Question

Mathematics

Guest

27 August, 21:39

An athlete suspected of having used steroids is given two tests that operate independently of each other. Test A has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroids have been used. What is the probability that atleast one test is positive if steroids have been used?

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Rory · Answer 1

0.82

Step-by-step explanation:

given that an athlete suspected of having used steroids is given two tests that operate independently of each other.

Test A has probability 0.9 of being positive if steroids have been used. Test B has probability 0.8 of being positive if steroids have been used.

A and B are independent of each other

Hence P (AB) = P (A) P (B)

Required probability = the probability that atleast one test is positive if steroids have been used

= P (AUB)

= P (A) + P (B) - P (AB)

= 0.9+0.8-0.9*0.8

= 0.82