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Math Help - Practical problem concerning expected value

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    Practical problem concerning expected value

    Hello!
    This is a video game related question, but please, take it seriously.
    Assume we have a lake consisting of 528 tiles and among them are 4 fixed tiles on which the player can catch a fish. There is also a fixed probability of catching a fish per one usage of fishing rod which is 35%. Essentially, using a rod is a Bernoulli trial with p=0.35 when fishing on a "fished" tile and p=0 on an empty tile. The player starts fishing on tile 1 and uses his rod k times. Then he moves to tile 2, uses his rod k times and repeats the procedure until he has fished on every tile in the lake. Then he simply starts again from tile 1 and so on... My problem is as following:

    After how many uses of the fishing rod on average will the player finally catch a fish with respect to k

    I've been thinking about this for a few days, but still can't find a solution.
    Also, I'm not interested in the result itself, but I'd like to know how exactly I should approach this kind of a problem.
    Last edited by Armadillomon; December 27th 2011 at 12:55 PM.
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