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Math Help - Independent probabilities question

  1. #1
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    Independent probabilities question

    Dear All,

    I am new to probability theory and it would be a great help if you can help me answering this question.


    There are N balls. There is a circle in the space. The probability of each ball to fall in the circle is p. What is the probability that there are *at least* k out of N balls that fall in the circle? I came up with the probability of at least one out of N balls falling in the circle and that is ( 1 - (1 - p)^N). Can someone please guide me how to do for k.


    Thanks ,
    Cheema
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  2. #2
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    Hello cheema

    Welcome to Math Help Forum!
    Quote Originally Posted by cheema View Post
    Dear All,

    I am new to probability theory and it would be a great help if you can help me answering this question.


    There are N balls. There is a circle in the space. The probability of each ball to fall in the circle is p. What is the probability that there are *at least* k out of N balls that fall in the circle? I came up with the probability of at least one out of N balls falling in the circle and that is ( 1 - (1 - p)^N). Can someone please guide me how to do for k.


    Thanks ,
    Cheema
    Looking at the title of your post, I'm assuming that the ways in which the balls fall are independent of each other, so this is an example of a Binomial Distribution.

    The probability of each trial resulting in a success is p, where a 'trial' is a ball falling and a 'success' is the ball falling into the circle. The number of trials is N, and we want the probability that the number of successes is greater than or equal to k.

    The formula that gives the probability of getting exactly r successes in N trials is:
    \binom Nrp^r(1-p)^{N-r}
    and we shall need the sum of all the terms like this, for values of r from k to N; in other words:
    \sum_{r=k}^N\binom Nrp^r(1-p)^{N-r}
    And that's it.

    Grandad
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  3. #3
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    That helped a lot. Thanks for answering in so clearly
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