Consider a binomial\((10,p)\) distribution. If \(p\) is chosen uniformly at random from the interval \((0,1)\), what is the likelihood that the most likely number of the binomial distribution will be less than the mean of the binomial distribution?

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Consider a binomial\((10,p)\) distribution. If \(p\) is chosen uniformly at random from the interval \((0,1)\), what is the likelihood that the most likely number of the binomial distribution will be less than the mean of the binomial distribution?