bayes_theorem_exercise.ipynb

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    "## Exercise 1\n",
    "In Orange County, 51% of the adults are males. (It doesn't take too much advanced\n",
    "mathematics to deduce that the other 49% are females.) One adult is randomly selected\n",
    "for a survey involving credit card usage.\n",
    "\n",
    "- **(a)** Find the probability that the selected person is a male.\n",
    "\n",
    "- **(b)** It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration). Use this additional information to find the probability that the cigar−smoking respondent is a male\n",
    "\n",
    "Use following notation:\n",
    "M = male <br>\n",
    "F = female <br>\n",
    "C = cigar smoker<br>\n",
    "NC = not a cigar smoker<br>\n"
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    "# Exercise 2\n",
    "\n",
    "A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering\n",
    "from a certain disease, and a probability 0.10 of giving a (false) positive when applied to a non-sufferer. It is\n",
    "estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about\n",
    "whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this\n",
    "population). \n",
    "\n",
    "Calculate the following probabilities:\n",
    "- **(a)** that the test result will be positive;\n",
    "- **(b)** that, given a positive result, the person is a sufferer;\n",
    "- **(c)** that, given a negative result, the person is a non-sufferer;\n",
    "- **(d)** that the person will be misclassified.\n",
    "\n",
    "Use following notation:\n",
    "\n",
    "T = test positive <br>\n",
    "NT = test negative<br>\n",
    "S = sufferer<br>\n",
    "NS = non-sufferer<br>\n",
    "M = misclassified<br>\n",
    "\n",
    "Solve it by two approaches:\n",
    "1. Arithmetically\n",
    "2. By simulation"
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