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Calculate the probabilities p 1 and p 2

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Reference no: EM13887222

Two duelists, A and B , take alternate shots at each other, and the duel is over when a shot (fatal or otherwise!) hits its target. Each shot fired by A has a probability α of hitting B , and each shot fired by B has a probability β of hitting

A . Calculate the probabilities P 1 and P 2 , defined as follows, that A will win such a duel: P 1 , A fires the first shot; P 2 , B fires the first shot.

If they agree to fire simultaneously, rather than alternately, what is the probability P 3 that A will win, i.e. hit B without being hit himself?

Reference no: EM13887222

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