MCQ_grading(Bayes).ipynb

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   "source": [
    "# Does MCQ Grading Really Judge Students Knowledge?"
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    "Grading a multiple choice exam is easy. But how much do multiple choice exams tell us about what a student really knows? Dr. Dirac is administering a statistics midterm exam and wants to use Bayes’ Theorem to help him understand the following:\n",
    "\n",
    "## - ***Given that a student answered a question correctly, what is the probability that she really knows the material?***"
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    "import numpy as np\n"
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    "Dr. Dirac knows the following probabilities based on many years of teaching:\n",
    "\n",
    "1. There is a question on the exam that 60% of students know the correct answer to.\n",
    "2. Given that a student knows the correct answer, there is still a 15% chance that the student picked the wrong answer.\n",
    "3. Given that a student does not know the answer, there is still a 20% chance that the student picks the correct answer by guessing. "
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    "### p(knows the material | answers correctly) ?\n",
    "\n",
    "\n",
    "####  Given:-\n",
    "-  p(knows the material) = 60 %\n",
    "-  p(wrong | knows material) = 15 %\n",
    "-  p(correct | don't know material) = 20 %\n"
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    "p_knows_material = 0.6\n",
    "\n",
    "p_wrong_given_knows_material = 0.15\n",
    "\n",
    "p_correct_given_ans_dont_know = 0.2"
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    "####  Calculation of:-\n",
    "-  P(Correct) = ?\n",
    "-  P(correct | knows material) = ?\n",
    "\n"
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    "p_correct_given_knows_material = 1 - p_wrong_given_knows_material\n",
    "\n",
    "p_correct = ((1 - p_knows_material) * (p_correct_given_ans_dont_know)) + (p_correct_given_knows_material * p_knows_material)"
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    "# Bayes Theorem\n",
    "\n",
    "$$P(Knows\\: Material\\: |\\: Correct) = \\frac{P(Correct\\: |\\: Knows\\: Material)\\:\\: P(Knows\\: Material\\:)} {P(Correct)}$$"
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    "p_knows_material_given_correct = (p_knows_material * p_correct_given_knows_material) / p_correct"
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     "text": [
      "86.44067796610169 % probability that,\n",
      "Correct answering students really knows the material\n"
     ]
    }
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   "source": [
    "print('{} % probability that,\\nCorrect answering students really knows the material'.format(p_knows_material_given_correct * 100))"
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