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

If y varies directly with x, x/y must remain the same for all valid values of x and y. So, x/y must equal 6/10 for all the values of y you posted. If y = 14, x = 8.4 because 8.4/14 = 6/10, and so on. (y = 14, x = 8.4), (y = 4.3, x = 2.58), (y = 8.4, x = 5.04), (y= 23.3, x = 13.98), and (y = 60, x = 36). Furthermore, to find a value of x for a given value of y, manipulate x/y = k to make the process even easier. What we want to do is isolate x. So, (x/y) * y = k * y, which simplifies to x = ky. Now, use it by plugging in the value of k, which is 6/10, and then plugging in the value of y that you need to find an x-value for. For example, if y = 14 it should look like this x = (6/10)(14). Now that you've done that, evaluate the equation, and you should arrive at x = 8.4.