@Salil: Just to make sure we are on the same page, A hits with 100% probability, B hits with 50% probability, and C hits with 33% probability. C shoots first, then B, then A. Then the shooting continues among the survivors in that order until only one is standing.
If all three are alive and it is A's turn to shoot, he logically will choose to shoot at B rather than C since B has a greater probability of hitting him. Thus, your P(A shooting at C) = 0 if B is unhit when it is A's turn. Similarly, if it is B's turn to choose between shooting at A or C, he rationally will choose A since A will shoot at and hit B if A gets a turn. So your P(B shooting at C) = 0 if A is unhit when it is B's turn. If you dispute either of the above two paragraphs, please clealy state your objection. Dave On Jan 1, 11:19 pm, Salil Joshi <[email protected]> wrote: > @Dave, > Yeah, I had read those numbers on internet as this puzzle is well known. > However I am not convinced with the calculations because of following 2 > points: > > 1) If C shoots in air, the probability of survival is more for the > probabilities considered in the calculations with which A & B will shoot at > him. > Now, if A & B are intelligent, they will know that increasing survival > probability for C is bad for them (you can calculate survival probability > for A & B in each case), and therefore they will shoot at C with higher > probability than what they were planning earlier. > > 2) C's survival probability depends on P(A shooting at C) * 1 and P(B > shooting at C) * 1/2. > If C shoots at A, P(A shooting at C) is less by 33% and P(B shooting at C) > is more by 33%. So, if P(A shooting at C) dominates by logic in 1st point, > C's survival probability will be now more. > > > > > > On Sun, Jan 2, 2011 at 7:59 AM, Dave <[email protected]> wrote: > > @Salil: Working out the probabilities, we find that: > > > 1. If C initially shoots at A, C's probability of survival is ~ > > 0.35867. > > 2. If C initially shoots at B, C's probability of survival is ~ > > 0.27679. > > 3. If C initially shoots in the air, C's probability of survival is ~ > > 0.49624. > > > Dave > > > On Jan 1, 11:30 am, Salil Joshi <[email protected]> wrote: > > > @Rahul, > > > As per my understanding, > > > In any round P(C is dead) = P(A is alive * A shoots C * A's shot is > > > accurate) + P(B is alive * B shoots C * B's shot is accurate) > > > this is to be minimized. > > > by not shooting at either A or B in 1st chance, how is this probability > > less > > > for C? > > > > On Sat, Jan 1, 2011 at 10:43 PM, Salil Joshi <[email protected] > > >wrote: > > > > > @Rahul, > > > > What purpose is served by wasting the shot? If C shoots at A or B, at > > least > > > > some probability that C is dead in future will be reduced. > > > > > On Sat, Jan 1, 2011 at 10:14 PM, RAHUL KUJUR < > > [email protected]>wrote: > > > > >> @snehal: > > > >> will the shooting take place in increasing order of accuracy of > > hitting > > > >> the target and is that at a time only one person can take a shot??? > > > >> if yes then > > > >> @Salil: > > > >> my answer would be the same as above. what C will do is that it will > > first > > > >> let A and B kill each other first. > > > >> After C wastes his shot it will be B's turn. B can kill C, but in that > > > >> case the turn would go to A and he would surely kill B. If B goes > > after A, > > > >> then B may hit it or miss it(as its probability of hitting is 50%) > > > >> If B misses it > > > >> then > > > >> it depends on A whom to kill. A may kill B or C. A will try to kill > > one > > > >> who is better shooter i.e. B as C is less likely to hit A. > > > >> If B hits A then we are done. Round 1 is complete(as required in the > > > >> question) and C survives the first round. > > > >> Look the problem is not that who gets killed at last but rather what C > > > >> should fire in the first round obviously to survive(as I understood > > the > > > >> problem). It may happen that eventually C gets killed. But what should > > C > > > >> shoot in first round to survive. > > > > >> -- > > > >> You received this message because you are subscribed to the Google > > Groups > > > >> "Algorithm Geeks" group. > > > >> To post to this group, send email to [email protected]. > > > >> To unsubscribe from this group, send email to > > > >> [email protected]<algogeeks%2bunsubscr...@googlegroups.com> > > <algogeeks%2bunsubscr...@googlegroups.com> > > > >> . > > > >> For more options, visit this group at > > > >>http://groups.google.com/group/algogeeks?hl=en. > > > > > -- > > > > > -------- > > > > Thanks & Regards > > > > Salil Joshi. > > > > CSE MTech II, IITB > > > > A-414, Hostel 12 > > > > +91.9819.442.865 > > > > > This is a confidential E-Mail. If it has reached you by mistake or if > > you > > > > are not the intended receiver, please send it back to me. > > > > -- > > > > -------- > > > Thanks & Regards > > > Salil Joshi. > > > CSE MTech II, IITB > > > A-414, Hostel 12 > > > +91.9819.442.865 > > > > This is a confidential E-Mail. If it has reached you by mistake or if you > > > are not the intended receiver, please send it back to me.- Hide quoted > > text - > > > > - Show quoted text - > > > -- > > You received this message because you are subscribed to the Google Groups > > "Algorithm Geeks" group. > > To post to this group, send email to [email protected]. > > To unsubscribe from this group, send email to > > [email protected]<algogeeks%2bunsubscr...@googlegroups.com> > > . > > For more options, visit this group at > >http://groups.google.com/group/algogeeks?hl=en. > > -- > > -------- > Thanks & Regards > Salil Joshi. > CSE MTech II, IITB > A-414, Hostel 12 > +91.9819.442.865 > > This is a confidential E-Mail. If it has reached you by mistake or if you > are not the intended receiver, please send it back to me.- Hide quoted text - > > - Show quoted text - -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
