8 cashews, 10 raisins and 5 figs are to be distributed among three people A.B.C. Three people D.E.F are appointed for the distribution of cashews, raisins and figs respectively. A.B.C are sitting in a room. D enters the room, distributes cashews among A,B,C and exits the room. E enters after D has left, distributes raisins and exits. Finally, F enters after E has left, distributes figs and leaves the room. D, E and F do not meet each other. However, there is a twist. Person A knows the total number of cashews, raisins and figs that are going to be distributed. F is allowed to distribute figs only if A gets at least half the total number of raisins to be distributed and E is allowed to distribute raisins only if A receives half or more than half of the total number of cashews to be distributed. What is the probability that A gets no fig?
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