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I encountered a set of problems while studying statistics for research which I have combined to get a broader question. I want to know if this is a solvable problem with enough information specifically under what assumptions or approach.

Given that a minesweeper has encountered exactly 5 landmines in a particular 10mile stretch, what is the probability that he will encounter exactly 6 landmines on the next 10mile stretch. (Average number of landmines is 0.6 per mile in the 50mile stretch)

I have figured that the approach involves finding out the Poisson probalities of the discrete random variable with the combination of Bayes Conditional probability. But am stuck with proceeding on applying the Bayes rule. i.e P(X=6/X=5)

I know that P(X=5) = (e^-6 * 5^6 ) / 5! Here lambda = .6 * 10 and X = 5) Similarly for P(X=6) IS Bayes rule useful here P(Y/A) = P(A/Y)*P(Y)/ (P(A/Y)*P(Y) + P(A/N)*P(N))

Would appreciate any hints on proceeding with these types of formulations.

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From the FAQ: "Math Overflow is not for homework help." Please see the other sites mentioned in the FAQ. –  Douglas Zare Sep 10 '11 at 8:38
    
Hello doug, I think you are mistaken here. I need this for my understanding this type of problem solving and not part of any homework. That is hwy I have mentioned the parts I have been able to analyse and need hints for the gaps in knowledge. I think this is what mathoverflow is for. –  user17710 Sep 10 '11 at 8:46
    
The point is that if you remove the ambiguity in your description of the problem, it becomes a simple exercise which is on the level of homework rather than of interest to mathematicians. "If you toss a coin 10 times and get heads 5 times, what is the probability you get 6 heads in the next 10 tosses?" That is very similar, and has the same ambiguity that you are not saying whether you know the coin is fair or not. –  Douglas Zare Sep 10 '11 at 21:14
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@unknown syko babel, see math.stackexchange.com/q/63285/6179 –  Did Sep 11 '11 at 11:07
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1 Answer 1

If this is assumed to be a (homogeneous) Poisson process with a known rate (namely 0.6 per mile), then the numbers in disjoint 10-mile stretches are independent. The number of mines in the first 10 miles is irrelevant.

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