(equation 1): P(D|S T) = P(D (S T)) / (P(S T)) <== I'm pretty sure this is right
Yes it isI *think* the denominator in equation 1 (P(S T)) should be 0.0593*0.0593 because the events are independent and equal, but I'm not sure about this.
Is this a correct assumption?
Stop hereP(S T|D) = P(S|D)P(T|D) = P(D (S T)) / P(D) <== this is given as a hint in the question.
Ok, this is true. But you have no clue what P(D (S T)) is.
So far, you have two equations :
P(D|S T) = P(D (S T)) / (P(S T))
P(S|D)P(T|D) = P(D (S T)) / P(D)
From the second equation, you have :
P(D (S T))=P(D)P(S|D)P(T|D)
By replacing in the first equation (the green one), you get :
Correct.we know (I think) that P(S|D) = P(T|D) = 0.98 (see above).
we also know that P(D) = 0.01 (above).
It's a bit messy because I tried to quote what you did so that you can see the reasoning, but you should be able to conclude with all of that