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shivani |
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#1
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Dedicated Member ![]() Group: Members Posts: 3886 Joined: 1-August 05 Member No.: 2848 ![]() |
1. Guess the next number
77 58 49 45 29 27 23 |
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shivani |
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Post
#2
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Dedicated Member ![]() Group: Members Posts: 3886 Joined: 1-August 05 Member No.: 2848 ![]() |
mmm..
When it is A's turn he can and will shot C with the probability 1. Therefore C has to maximise the probability that A is shot. If C shoots in the air the probability A is shot is 0.5 If C shoots at B than there is 2/3 probability B survives and shoots at A. In this case A is shot with the probability 2/3 * 0.5 = 1/3. The best strategy for C is to shoot in the air. survival probability for C when he shoots in air for first time - (1/3 + 1/2)/2 = 5/12 This number needs to be compared with the Kill A scenario. (Killing B is obviously bad.) If C kills A, C's survival probability is 1- (1/2 + 1/2 * 1/3 + 1/2 * 1/3^2 + 1/2*1/3^3...) = 1/4. Since 1/4 < 5/12, shooting in the air is correct. |
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