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# Help with a simple probability problem watch

1. Pretty sure this is fairly simple and I'm just being a total idiot right now as I haven't done probability in ages, but can someone help me with this:

"Suppose that I think the probability that a certain particle exists is 0.2. Furthermore my theory tells me that if the particle exists the probability that a certain experiment succeeds is 0.8, whereas if the particle doesn't exist the probability of success is 0.05. The experiment does succeed. How probable should I think it that the particle exists now?"

How do I work out what the probability of the experiment succeeding, period, given nothing, is?
2. (Original post by TorpidPhil)
Pretty sure this is fairly simple and I'm just being a total idiot right now as I haven't done probability in ages, but can someone help me with this:

"Suppose that I think the probability that a certain particle exists is 0.2. Furthermore my theory tells me that if the particle exists the probability that a certain experiment succeeds is 0.8, whereas if the particle doesn't exist the probability of success is 0.05. The experiment does succeed. How probable should I think it that the particle exists now?"

How do I work out what the probability of the experiment succeeding, period, given nothing, is?
If E is the event "the particle exists" and X is the event "the experiment succeeds" then what you have been given is P(E), P(X|E) and P(X| ~E). You should now be able to work out P(X) by using the law of total probability.
3. (Original post by Gregorius)
If E is the event "the particle exists" and X is the event "the experiment succeeds" then what you have been given is P(E), P(X|E) and P(X| ~E). You should now be able to work out P(X) by using the law of total probability.
Yeah, that's what I can't do because I suck at probability and it is making my mind trip up for no apparent reason :P
4. (Original post by torpidphil)
yeah, that's what i can't do because i suck at probability and it is making my mind trip up for no apparent reason
p(x) = p(x|e)p(e) + p(x|~e)p(~e)
5. (Original post by Gregorius)
p(x) = p(x|e)p(e) + p(x|~e)p(~e)
Than you sir

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