Therefore, the probability of A losing if he aims at C first is: (1/3)(6/7)+2/3[(2/3)(4/7)+(1/3)(2/3)] =130/189. So if A aims at C he will only have a 49/189 (31%) chance of winning.
If A deliberately misses: If B hits C, then A and B will duel to the death, with A going first. If B misses C, then C will kill B and A will have aim at C, if A misses C will kill A. Therefore the probability of A losing if he deliberately misses is:
P(B hits C) x P(B wins duel when A goes first) + P(B misses C) x P(A misses C)
= (2/3)(4/7) + (1/3)(2/3) = 38/63
So if A deliberately misses, he will have a 25/63 (40%) chance of winning, the best chance by some margin! To put it simply, A deliberately missing guarantees that he will have the first shot in a 2 way duel, either with B or C (because B or C will aim at each other). If aims at B or C then there is always the possibility that he will be a in a 2 way duel, but not shooting first, which is clearly a disadvantage.
Puzzle No.1
How can I get the answer 24 by only using the numbers 8,8,3,3. You
can use add, subtract, multiply, divide, and parentheses.
Bonus rules: also allowed are logarithms, factorials and roots
9
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