A person takes 4 tests in succession. The probability of his passing the first test is p, that of his passing each succeeding test is p or `p/2` depending on his passing or failing the preceding test, Find the probabilty of his passing
at least three test

A person takes 4 tests in succession. The probability of his passing the first test is p, that of his passing each succeeding test is p or p/2 depending on his passing or failing the preceding test, Find the probabilty of his passing just three tests.

A person takes 3 tests in succession. The probability of his (her) passing the first test is 0.8. The probability of passing each successive test is 0.8 or 0.5 according as he passes or fails the preceding test. Find the probability of his (her) passing at least 2 tests.

A laboratory blood test is 99% effective in detecting a certain disease,when it is infact present. However, the test also yields a false positive result for 0.5% of the healthy person tested (ie. if a healthy person is tested, then with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, then what is the probability that a person has disease, given that his test result is positive?

If P is the point (2,1,6), then find the point Q such that PQ is perpendicular to the plane passing through the points (2,1,0), (5,0,1), (4,1,1) and the mid point of PQ lies on it.

An examination was conducted in physics, chemistry and mathematics. If P.C.M. denote respectively the sets of students who passed in Physics, in Chemistry and in Mathematics, express the set of candidates who failed in Mathematics but passed in at least one subject using union , intersection and different symbols.

A person passes much urine and deink much water but his blood glucose level is normal. This condition may be the result of: