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We know that the famous birthday problem states that for a group of 23 people, there is a ~50% chance that two of them have the same birthday. However we can't say that the probability that two of them have a birthday on 1 January is 50%.
One way to approach this is to say that the probability of any one student having a birthday on 1 January is 1/365 (ignoring leap years). We want two or more students, so the probability is given by
binomcdf(23, 1/365, 2, 23)