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  text: '[summary: A probability distribution on a countable [3t4] $\\Omega$ is a [3jy] $\\mathbb{P}: \\Omega \\to [0,1]$ such that $\\sum_{\\omega \\in \\Omega} \\mathbb{P}(\\omega) = 1$.]\n\nDefinition\n===\n\nA probability distribution on a countable [3t4] $\\Omega$ is a [3jy] $\\mathbb{P}: \\Omega \\to [0,1]$ such that $\\sum_{\\omega \\in \\Omega} \\mathbb{P}(\\omega) = 1$. \n\nIntuition\n=====\n\nWe express a belief that "$x\\in \\Omega$ happens with probability $r$" by setting $\\mathbb{P}(x) = r$. So a probability distribution divides up our anticipation of what will happen, out of the set $\\Omega$ of things that might possibly happen.\n\n[todo: examples, futher points]\n',
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