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Maths challenge


Posts: 30

new Posted: 08:22PM Oct 4, 2015

JQP: The participants definitely do not target each other randomly (that was part 1 of the question). It's been long enough since I asked the question that I no longer have my notes on the probability, but you should assume that C shoots in the air/ground on the first round (because killing either of the other two would put him at a major disadvantage by giving a better marksman the first shot at C), B shoots at A (the bigger threat), and if B misses, A will shoot and kill B (again, the bigger threat). Take the probability calculation from there.
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Posts: 1900

new Posted: 08:24AM Oct 6, 2015

That was... much easier.

P(C survives|B's first shot succeeds) = (1/3) / (1 - 2/9) = 3/7

P(C survives|B's first shot fails) = 1/3

By theorem of total probability,
P(C survives) = 2/3 * 3/7 + 1/3 * 1/3 = 25/63

'An idea, like a ghost, must be spoken to a little before it will explain itself.' - Charles Dickens
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