Referring to the image , i have understood how probabilities are assigned to elements of sample space , S . Now , when we aim to calculate P(E|F) we consider F to be our new sample space for event E . So how do we assign the probabilities now to the elements of set F (like it was done for elements of S) ? Because i want to simply add P((T,5)) and P((T,6)) ,that is using the axiomatic theory of probability to get P(E|F) without using P(E and F )/P(F) which is the conventional formula to calculate conditional probability . I tried it a lot but wasn't able to do it .I just tried to back calculate it from the given answer for P(E|F) Which is 2/9 ( they used the formula ) , which implies that P((T,5)) and P((T,6)) are 2/9*1/2 which is 1/9 . So all of the P((T,i)) are 1/9 which makes it 2/3 and the one remaining P((H,T)) is 1/3 considering F as the sample space . But how do we determine directly these probabilities which i back calculated . Someone please help .