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Thread: A little help with what seems to be conditional probability

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    Lightbulb A little help with what seems to be conditional probability




    Hey guys, I want to make sure that I'm working this question correctly. Here goes:

    A jar has 5 white balls. A ball is taken out randomly - if it's white, a black ball is inserted instead, and we continue to take balls out. If it's black, we stop.

    Whats the probability that we will take 6 balls out until we stop?

    So I actually drew it out and treated the event of '6 balls out' as 'we take out all the white ones' and ended up multiplying each probability of taking a white out at each stage.
    So - at first we have 5/5 chance of getting a white one out, multiplied by 4/5 chance, 3/5... etc.

    Is this a correct way to solve this? I don't know why but it seems iffy really.

    Thanks alot!

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    Re: A little help with what seems to be conditional probability

    I always start by saying I am only OK with probabilities, but yes your approach seems correct. 5/5 * 4/5 * 3/5 * 2/5 * 1/5 * 5/5.
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    Re: A little help with what seems to be conditional probability

    Your other post made me revist this one. I believe this is correct, except the last 5/5 would be 0/5 and ignored since it does not make sense to test an impossibility.
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    Re: A little help with what seems to be conditional probability


    Quote Originally Posted by hlsmith View Post
    except the last 5/5 would be 0/5 and ignored since it does not make sense to test an impossibility.
    Nope. The only way to draw six balls is for the last ball to be black. The probability that the last ball is black in this case is 1.
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