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Thread: Question on probabilities

  1. #1 Question on probabilities 
    Forum Freshman
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    Consider the following example:

    1) The starting point is A
    2)The probability to go from A to B is 3/5
    3)The probability to go from A to C is 1/5
    4)The probability to stay at A is 1/5
    5)If you are at B you can never return to A
    6)There is no direct way from B to C
    7) There is an infinite number attempts to reach C

    What is the probability of ever reaching point C?

    i would suggest its 4/15, what do you think?


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  3. #2  
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    The probability of staying at A after an infinite number of attempts is 0. You will either end up at B or C. The probability of going to B is 3 times the probabilty of going to C. So I think the answer is 0.25.


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  4. #3  
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    my idea was to splitt the 1/5 probability of remaining at point A in a ratio (1/5)/(4/5) and to add it to the 1/5 probability of reaching point C. you are right it is 0.25.

    thanks harold
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  5. #4  
    . DrRocket's Avatar
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    Quote Originally Posted by Harold14370
    The probability of staying at A after an infinite number of attempts is 0. You will either end up at B or C. The probability of going to B is 3 times the probabilty of going to C. So I think the answer is 0.25.
    Correct, and nice reasoning.

    Another way to reach the same conclusion is to model the process as a Markov chain and note that at each step the probbility of going to C is 1/5 and the probability of the chain going to another state from which C can be reached is also 1/5. So the probability of reaching C eventually is .
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