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?

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