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Notation question

  1. Feb 7, 2008 #1
    My book uses this certain notation, but doesn't seem to explain it. It's probably something that I should already know...

    Bill and George (Noice!) go target shooting at each other. Both shoot at the target at the same time. Bill hits target with prob 0.7 and G independently hits target with prob 0.4.

    (a) Given that exactly one shot hit the target, what is the prob it was G's shot?

    [sol]

    P{G|exactly 1 hit} = P{G, not Bill}/ P(exactly 1 hit}

    = P{G, B'}/(P{G,B'} + P{B,G'})

    = [tex]\frac{P(G)P(B^{c})}{(P(G)P(B^{c}) + P(B)P(G^{c})}[/tex]

    I think the reason I don't follow is a notation thing. Can I treat the P{G, not Bill} as P(G[tex]\wedge[/tex]B[tex]^{c}[/tex])? If that's the case then it makes perfect sense as the events are independent.

    (b) Given that the target was hit, what's the probability it was G's shot?

    P(G|H) = P(G)/P(H)

    where

    P(H) = 1- P(no hit) = 1 - (P(G')P(B'))

    Why is it not P(G|H) = P(G)/P(G)P(B) ?
     
  2. jcsd
  3. Feb 7, 2008 #2

    EnumaElish

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    P{G, not Bill} = P(G and B') is correct.

    I don't understand your last question.
     
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