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Math Help - HELP! Assignment Question, Probability of Two people having the same birthday

  1. #1
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    Question HELP! Assignment Question, Probability of Two people having the same birthday

    The Question is as follows:
    Statisticians are prone to trying to impress their friends with random facts that
    may not be mathematically intuitive. One such fact that is repeated ad nauseum
    relates to the probability of people sharing a birthday. The common claim is that
    the probability of at least two people sharing a birthday in a room of randomly
    selected people is already more than 50% when there are only 25 people in the
    room and more than 99% when there are only 60 people in the room. The goal
    of this problem is to understand where this claim comes from and propose a slight
    modi cation to more accurately calculate these probabilities.
    To calculate the probability of at least two people sharing a birthday, there are two
    assumptions that are typically made:
     The year consists of 365 days, so leap years cannot happen and February 29 is
    ignored.
     Births occurs uniformly over the year. This means that the probability of
    having a birthday of March 2 is the same as that of having a birthday of
    November 21 (or any other date, for that matter).
    For the rst part of this problem, we will work under these two assumptions.
    (a) Calculate the probability of at least two people sharing a birthday in a room
    of 1, 2, : : :, 5 randomly chosen people. Then produce a general formula for
    calculating this probability for a room consisting of n randomly chosen people
    (for n  1), and use this to calculate the probability for rooms consisting of
    25 and 60 people to verify the claim. Note that you must use R to carryout probability calculations, and both your R code and output must
    be included with your answer.


    The most recent formula I came up with:

    A[i] = (choose(i,2)*choose(365,1)^(i-1)*choose(1,1))/365^i

    I have been stuck on this for far too long if someone could point me in the right direction that would be very helpful. Thanks
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  2. #2
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    Re: HELP! Assignment Question, Probability of Two people having the same birthday

    Thanks from stripe501
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