I'm stumped on this question.
Conditions:
Let PPVa = P[D|Ta]
Let PPVb = P[D|Tb intersection Tb]
Let SigmaA = P[Ta|D] = P[Ta|D intersection Tb]
Let KappaA = P[Ta complement|D complement]
Let SigmaB = P[Tb|D]
Let KappaB = P[Tb complement|D complement]
P[D|Ta intersection Tb] > P[D|Ta]
Attempt at a solution:
P[D intersection Ta intersection Tb]/P[Ta intersection Tb] > P[D intersection Ta]/P[Ta] (by condtional probability)
P[D]P[Tb|D]P[Ta|D intersection Tb]/P[Ta intersection Tb] > P[D]P[Ta|D]/P[Ta] (by event composition)
P[Tb|D]/P[Ta intersection Tb] > 1/P[Ta]
P[Tb|D] > P[Ta intersection Tb]/P[Ta]
SigmaB > P[Tb|Ta] (by conditional probability)
I don't know where to go from there. Some help would be greatly appreciated. The answer is supposed to be: SigmaB > 1 - KappaB.