Probabilities

probabilities.ipynb

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    "# Probabilities\n",
    "\n",
    "$X$ and $Y$ are events such that $X,Y \\in A$ where $A$ is the set of events.\n",
    "\n",
    "## Probability of an event\n",
    "The probability of an event $X$ in an event space $A$: $P(X) = count(X) / count(A)$\n",
    "\n",
    "## Probability of two events\n",
    "Probability of event $X$ and event $Y$ in event space $A$: $P(X and Y) = count(X and Y) / count(A)$\n",
    "\n",
    "## Conditional probability\n",
    "Probability of $X$ given $Y$: \n",
    "$$ P(X|Y) = \\frac{P(X and Y)}{P(Y)} $$\n",
    "\n",
    "## Propability of independant events\n",
    "Probability of $X$ and $Y$ when they are independent: $ P(XY) = P(X) + P(Y)$\n",
    "\n",
    "## Probability of dependent events\n",
    "Probability of $X$ and $Y$ when they are dependent: $ P(XY) = P(X) \\times P(Y) $\n",
    "\n",
    "## Bayes theorem\n",
    "$$ P(X|Y) = \\frac{P(Y|X)P(X)}{P(Y)}$$"
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