Solving Notation Question: Probability of G's Shot

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In summary: Can you clarify?In summary, the conversation discusses target shooting between Bill and George, with probabilities of hitting the target being 0.7 and 0.4 respectively. The question is asked about the probability of George's shot hitting the target if exactly one shot hit. The solution involves using conditional probability and treating P{G, not Bill} as P(G and B'), since the events are independent. The second question asks about the probability of George's shot hitting the target given that the target was hit, with the solution involving finding the probability of no hit and subtracting it from 1. The notation used may be confusing, but it can be simplified by treating P{G, not Bill} as P(G and B').
  • #1
Somefantastik
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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) ?
 
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  • #2
P{G, not Bill} = P(G and B') is correct.

I don't understand your last question.
 

Related to Solving Notation Question: Probability of G's Shot

What is the "Solving Notation Question: Probability of G's Shot"?

The Solving Notation Question: Probability of G's Shot is a mathematical problem that involves using notation and probability to determine the chances of a specific event occurring, in this case, G making a shot.

What are the steps for solving this notation question?

The steps for solving this notation question may vary depending on the specific problem, but generally, it involves identifying the given information and variables, setting up the notation equation, and solving for the probability using the given formula or rules of probability.

What is notation in probability?

Notation in probability refers to the symbols and mathematical expressions used to represent the likelihood of an event occurring. This can include symbols such as P (probability), n (number of trials), and x (number of successes).

What is the difference between theoretical probability and experimental probability?

Theoretical probability is the probability of an event occurring based on mathematical principles and assumptions, while experimental probability is the probability of an event occurring based on actual data and experiments. Theoretical probability is usually more accurate, but experimental probability can provide real-world insights.

What are some real-life applications of solving notation questions using probability?

Solving notation questions using probability can have various real-life applications, such as predicting the likelihood of a disease outbreak, determining the chances of winning a game, and calculating the probability of a stock market trend. It is also commonly used in fields such as finance, insurance, and science.

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