Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. Represent the "74.6%" using notation.

O P(S)
O P(S and POS)
O P(POS)
O P(POS I S)

P(POS/S)

Explanation:

Here, P(S) represents the probability that the adult really has tuberculosis,

P(S and POS) represents the probability that the adult really has tuberculosis and the test gives a positive result.

P(POS) represents the probability the test gives a positive result.

Finally, P(POS/S) represents the probability that the test correctly identifies adults with tuberculosis, which is exactly 74.6%.    

these are common warning signs of overtraining syndrome:

washed-out feeling, tired, drained, lack of energy

mild leg soreness, general aches, and pains

pain in muscles and joints

sudden drop in performance

insomnia

headaches

decreased immunity (increased number of colds, and sore throats)

decrease in training capacity/intensity

moodiness and irritability

depression

loss of enthusiasm for the sport

decreased appetite

increased incidence of injuries.

a compulsive need to exercise

a1 = unhealthy

a2= healthy

a3= healthy