Lesson-Statistics and Probability XV-Conditional Probability.ipynb

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    "# Lesson - Statistics and Probability XV: Conditional Probability Fundamentals\n",
    "\n",
    "**Recap**\n",
    "\n",
    "We have already seen that a random experiment such as rolling a six sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6. The set of all possible outcomes associated with a random experiment is called a sample space, and we denote it by the Greek letter Ω (\"Omega\"). We represent the sample space of a die roll as a set:\n",
    "$$\\begin{equation}\n",
    "\\Omega = \\{1, 2, 3, 4, 5 ,6\\}\n",
    "\\end{equation}$$\n",
    "\n",
    "Under the assumption that all six outcomes are equally likely (the die is fair), we can find P(5) — the probability of the event \"getting a 5\" — by using the following formula:\n",
    "$$\\begin{equation}\n",
    "\\text{P(5)} = \\frac{\\text{number of successful outcomes}}{\\text{total number of possible outcomes}}\n",
    "\\end{equation}$$\n",
    "\n",
    "There are six possible outcomes (1, 2, 3, 4, 5, and 6) and one successful outcome (5), so the probability of getting a 5 when rolling a fair six-sided die is:\n",
    "$$\\begin{equation}\n",
    "\\text{P(5)} = \\frac{\\text{number of successful outcomes}}{\\text{total number of possible outcomes}} = \\frac{1}{6}\n",
    "\\end{equation}$$\n",
    "\n",
    "Here we will discuss probability based on certain conditions based on conditional probability rules."
   ]
  },
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Updating Probability\n",
    "If in the above random experiment, the die showed an odd number (1, 3, or 5) after landing, and we know that the number is \"Odd\", then the probability of \"getting a 5\" changes in the light of the new knowledge.\n",
    "\n",
    "When we don't know whether the number is odd, the possible outcomes of the experiment are 1, 2, 3, 4, 5, or 6. But after we find out the number is odd, the possible outcomes are 1, 3, or 5. In other words, the new information we got reduced the sample space from {1, 2, 3, 4, 5, 6} to {1, 3, 5}:\n",
    "$$\\begin{equation}\n",
    "\\Omega = \\{1, 2, 3, 4, 5, 6\\}\\ \\ \\ \\ \\xrightarrow[]{becomes} \\ \\ \\ \\ \\Omega = \\{1, 3, 5\\}\n",
    "\\end{equation}$$\n",
    "\n",
    "With Ω = {1,3,5}, we now have three total possible outcomes (1, 3, and 5) and only one successful outcome (5), so P(5)≠ 1/6 , but rather:\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "A fair six-sided die is rolled. All we know is that the number we got is less than 5. Calculate:\n",
    "\n",
    "- The probability of getting a 3. Assign answer to `p_3`.\n",
    "- The probability of getting a 6. Assign answer to `p_6`.\n",
    "- The probability of getting an odd number. Assign answer to `p_odd`.\n",
    "- The probability of getting an even number Assign answer to `p_even`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_3 = 1/4\n",
    "p_6 = 0\n",
    "p_odd = 2/4\n",
    "p_even = 2/4\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conditional Probability##\n",
    "\n",
    "Above, we considered a die roll and updated P(5) from 1/6 to 1/3. Taken individually, however, are correct answers to different questions:\n",
    "\n",
    "- What is the probability of getting a 5?\n",
    "- What is the probability of getting a 5 given the die showed an odd number?\n",
    "\n",
    "P(5) = 1/6 is a correct answer to the first question, where we only want to find the probability of getting a 5. P(5) = 1/3 is a correct answer to the second question, where we introduce a condition: the die showed an odd number. To account for this condition and for the fact that two different questions are being addressed, we have to introduce some extra notation:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\text{P}(5) = \\frac{1}{6}\n",
    "\\\\\n",
    "\\text{P}(5\\underbrace{\\text{ given the die showed an odd number}}_{\\text{extra notation}}) = \\frac{1}{3}\n",
    "\\end{equation}$$\n",
    "\n",
    "For notation simplicity, $\\text{P}(5 \\text{ given the die showed an odd number})$ becomes $\\text{P}(5\\ | \\text{ odd})$. The vertical bar character (|) should be read as \"given.\" Another way to read $\\text{P}(5\\ | \\text{ odd})$ is the conditional probability of getting a 5 given the die showed an odd number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "A student is randomly selected from a class. All we know is that he was born during winter. Assume the winter months are December, January, and February and ignore the fact that these three months have different number of days. Find:\n",
    "\n",
    "- The probability that he was born in December. Assign your answer to `p_december`.\n",
    "- The probability that he was born in a 31-day month. Assign answer to `p_31`.\n",
    "- The probability that he was born during summer. Assign answer to `p_summer`.\n",
    "- The probability that he was born in a month which ends in letter \"r\" — \"September,\" for instance, ends in \"r,\" while \"April\" doesn't. Assign answer to `p_ends_r`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_december = 1/3\n",
    "p_31 = 2/3\n",
    "p_summer = 0\n",
    "p_ends_r = 1/3"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Conditional Probability Formula**\n",
    "\n",
    "If we roll a fair six-sided die and want to find the probability of getting an odd number, given the die showed a number greater than 1 after landing. Using probability notation, we want to find P(A|B) where: \n",
    "\n",
    "- A is the event that the number is odd: A = {1, 3, 5}\n",
    "- B is the event that the number is greater than 1: B = {2, 3, 4, 5, 6}\n",
    "\n",
    "To find P(A|B), we need to use the following formula:\n",
    "$$\\begin{equation}\n",
    "P(A|B) = \\frac{\\text{number of successful outcomes}}{\\text{total number of possible outcomes}}\n",
    "\\end{equation}$$\n",
    "\n",
    "We know for sure event B happened (the number is greater than 1), so the sample space is reduced from {1, 2, 3, 4, 5, 6} to {2, 3, 4, 5, 6}:\n",
    "$$\\begin{equation}\n",
    "\\Omega = \\{1, 2, 3, 4, 5, 6\\} \\xrightarrow[]{becomes} \\Omega = \\{2, 3, 4, 5, 6\\}\n",
    "\\end{equation}$$\n",
    "\n",
    "This means we're left with only five total possible outcomes if B happens:\n",
    "$$\\begin{equation}\n",
    "\\text{total number of possible outcomes} = 5\n",
    "\\end{equation}$$\n",
    "The total number of possible outcomes above is given by the number of elements in the reduced sample space $\\Omega = \\{2, 3, 4, 5, 6\\}$ — there are five elements.\n",
    "\n",
    "The number of elements in a set is called the cardinal of the set. Ω is a set, and the cardinal of Ω = {2,3,4,5,6} is $\\begin{equation}\n",
    "\\text{cardinal}(\\Omega) = 5\n",
    "\\end{equation}$ In set notation, cardinal(Ω) is abbreviated as card(Ω), so we have: \n",
    "$$\\begin{aligned}\n",
    "\\text{total number of possible outcomes} &= \\text{card(B)} \\\\\n",
    "&= 5\n",
    "\\end{aligned}$$\n",
    "\n",
    "So far, we've developed half of our formula:\n",
    "$$\\begin{equation}\n",
    "P(A|B) = \\frac{\\text{number of successful outcomes}}{\\text{card(B)}}\n",
    "\\end{equation}$$\n",
    "\n",
    "There are three odd numbers on a regular six-sided die (1, 3, and 5), but we know for sure we got a number greater than 1, so the only possible odd numbers we can get are 3 and 5. This means that the number of possible successful outcomes is two.\n",
    "\n",
    "The only possible odd numbers we can get are only 3 and 5, and the number of possible successful outcomes is also given by the cardinal of the set {3, 5}. Note that the set {3, 5} is the result of the intersection between set A and set B:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "So the number of successful outcomes is given by the cardinal of the intersection between set A and B:\n",
    "$$\\begin{aligned}\n",
    "\\text{total number of possible outcomes} &= \\text{card(A} \\cap \\text{B)} \\\\\n",
    "&= \\text{card({3,5})} \\\\\n",
    "&= 2\n",
    "\\end{aligned}$$\n",
    "\n",
    "We can plug that into our formula and calculate P(A|B):\n",
    "$$\\begin{aligned}\n",
    "P(A\\ |\\ B) &= \\frac{\\text{card(A} \\cap \\text{B)}}{\\text{card(B)}} \\\\\n",
    "&= \\frac{2}{5}\n",
    "\\end{aligned}$$\n",
    "\n",
    "We now have a formula for conditional probability, defined purely in terms of A and B, where A and B can be any events (not just events related to a die roll)."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "Two fair six-sided dice are simultaneously rolled, and the two numbers they show are added together. The diagram below shows all the possible results that we can get from adding the two numbers together.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Find P(A|B), where A is the event where the sum is an even number, and B is the event that the sum is less than eight.\n",
    "\n",
    "- Find card(B). Assign answer to `card_b`.\n",
    "- Note that for calculating cardinal, we'll have to treat identical sums differently if they come from different die numbers. On the diagram above, we see that we have three sums of 4, but they all come from different die outcomes: (3, 1), (2,2), and (1, 3), where the first number describes the outcome of the first die throw, and the second number the outcome of the second die throw.\n",
    "- Find card(A ∩ B). Assign answer to `card_a_and_b`.\n",
    "- Calculate P(A|B). Assign answer to `p_a_given_b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "card_b = 21\n",
    "card_a_and_b = 9\n",
    "p_a_given_b = 9/21"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example**\n",
    "\n",
    "A team of biologists wants to measure the efficiency of a new HIV test they developed (HIV is a virus that causes AIDS, a disease which affects the immune system). They used the new method to test 53 people, and the results are summarized in the table below:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "By reading the table above, we can see that:\n",
    "\n",
    "- 23 people are infected with HIV.\n",
    "- 30 people are not infected with HIV (HIVC means not infected with HIV — the superscript \"C\" indicates a set complement).\n",
    "- 45 people tested positive for HIV .\n",
    "- 8 people tested negative for HIV.\n",
    "- Out of the 23 infected people, 21 tested positive (correct diagnosis).\n",
    "- Out of the 30 not-infected people, 24 tested positive (wrong diagnosis).\n",
    "\n",
    "\n",
    "The team now intends to use these results to calculate probabilities for new patients and figure out whether the test is reliable enough to use in hospitals. They want to know:\n",
    "\n",
    "- What is the probability of testing positive, given that a patient is infected with HIV?\n",
    "- What is the probability of testing negative, given that a patient is not infected with HIV?\n",
    "\n",
    "P(T+ | HIV) is the probability of testing positive, given that the patient is infected with HIV, and, according to the formula, we have:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(T^+|HIV) = \\frac{card(T^+ \\cap HIV)}{card(HIV)}\n",
    "\\end{equation}$$\n",
    "\n",
    "There are 23 people infected with HIV, which means card(HIV) = 23, out of these 21 are tested positive meaning $card(T^+ \\cap HIV) = 21$ = 21. \n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "This means that P(T+ | HIV) is:\n",
    "$$\\begin{equation}\n",
    "P(T^+|HIV) = \\frac{21}{23} = 0.9130\n",
    "\\end{equation}$$\n",
    "\n",
    "The probability of testing positive, given that the patient is infected with HIV, is therefore 91.30% — this may suggest that the new test is fairly good at detecting the HIV virus when the virus is actually present. However, at a probability of 91.31%, we can expect that for every 10,000 patients infected with HIV, about 9,131 patients will get a correct diagnosis, while the other 869 will not. The team should probably conclude that the test needs more refinement with respect to detecting the virus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "Use the data in the table above and :\n",
    "\n",
    "- Calculate P(T- | HIVC). Assign answer to `p_negative_given_non_hiv`.\n",
    "- Print `p_negative_given_non_hiv`.\n",
    "- Interpret the result — does the value of P(T- | HIVC) suggest that the test needs more work? Or does it look like the test is reliable enough to use in hospitals?\n",
    "\n",
    "Ans. \n",
    "card(non_hiv) = 30\n",
    "card(T- given non_hiv) = 6\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2\n"
     ]
    }
   ],
   "source": [
    "p_negative_given_non_hiv = 6/30\n",
    "print(p_negative_given_non_hiv)\n",
    "# The team needs to do more work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Formula (in terms of probabilities)\n",
    "\n",
    "Above, we used our formula and saw that P(T+ | HIV) — the probability of testing positive, given that the patient is infected with HIV — is:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(T^+ | HIV) = \\frac{card(T^+ \\cap HIV)}{card(HIV)} = \\frac{21}{23}\n",
    "\\end{equation}$$\n",
    "\n",
    "Note, however, that we'd arrive at the same result if we used probabilities instead of cardinals. Using the table above, we see that:\n",
    "\n",
    "$P(T^+ \\cap HIV) = \\frac{21}{53}$ and $P(HIV) = \\frac{23}{53}$ This means that:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(T^+ | HIV) = \\frac{P(T^+ \\cap HIV)}{P(HIV)} = \\frac{\\frac{21}{53}}{\\frac{23}{53}} = \\frac{21}{23}\n",
    "\\end{equation}$$\n",
    "\n",
    "This allows us to define a formula for conditional probability purely in terms of probabilities instead of set cardinals. Thus, for any two events A and B, P(A|B) is:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(A | B) = \\frac{\\text{P(A} \\cap \\text{B)}}{\\text{P(B)}}\n",
    "\\end{equation}$$\n",
    "\n",
    "This formula is useful when we only know probabilities. For instance, let's say a **different test** is used to diagnose a patient. The patient tests positive for HIV, and we want to find P(HIV | T+) — the probability that the patient actually has HIV, given that the test was positive.\n",
    "\n",
    "This time, however, all we know is P(T+) = 0.12 and $P(HIV \\cap T^+) = 0.000015# We can no longer find cardinals, but using the formula above, we have:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(HIV | T^+) = \\frac{P(HIV \\cap T^+)}{P(T^+)} = \\frac{0.000015}{0.12} = 0.000125\n",
    "\\end{equation}$$\n",
    "\n",
    "To understand the mathematical reason for why the above formula works, let's start by considering the following mathematical statements:\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\tag{1} P(A \\cap B) = \\frac{\\text{number of successful outcomes}}{\\text{total number of possible outcomes}} = \\frac{card(A \\cap B)}{card(\\Omega)}\n",
    "\\end{equation}$$\n",
    "\n",
    "$$\\begin{equation}\n",
    "\\tag{2} P(B) = \\frac{\\text{number of successful outcomes}}{\\text{total number of possible outcomes}} = \\frac{card(B)}{card(\\Omega)}\n",
    "\\end{equation}$$\n",
    "\n",
    "Given statements (1) and (2) above, we have:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(A|B) = \\frac{\\frac{card(A \\cap B)}{card(\\Omega)}}{\\frac{card(B)}{card(\\Omega)}} = \\frac{P(A \\cap B)}{P(B)}\n",
    "\\end{equation}$$\n",
    "\n",
    "Both card(Ω) cancel out, so we're left with:\n",
    "\n",
    "$$\\begin{equation}\n",
    "P(A|B) = \\frac{card(A \\cap B)}{card(B)} = \\frac{P(A \\cap B)}{P(B)}\n",
    "\\end{equation}$$"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**\n",
    "\n",
    "A company offering a browser-based task manager tool intends to do some targeted advertising based on people's browsers. The data they collected about their users is described in the table below:\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Find:\n",
    "\n",
    "- P(Premium | Chrome) — the probability that a randomly chosen user has a premium subscription, provided their browser is Chrome. Assign answer to `p_premium_given_chrome`.\n",
    "- P(Basic | Safari) — the probability that a randomly chosen user has a basic subscription, provided their browser is Safari. - Assign answer to `p_basic_given_safari`.\n",
    "- P(Free | Firefox)} — the probability that a randomly chosen user has a free subscription, provided their browser is Firefox. Assign answer to `p_free_given_firefox`.\n",
    "- Between a Chrome user and a Safari user, who is more likely to have a premium subscription? If a Chrome user is the answer, then assign the string 'Chrome' to a variable named `more_likely_premium`, otherwise assign 'Safari'. To solve this exercise, we'll also need to calculate P(Premium | Safari)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Safari\n"
     ]
    }
   ],
   "source": [
    "p_premium_given_chrome = (158/2762) \n",
    "\n",
    "p_basic_given_safari = (274/ 1288) \n",
    "\n",
    "p_free_given_firefox = (2103 / 2285)\n",
    "\n",
    "p_premium_given_safari = (120/1288) \n",
    "\n",
    "if p_premium_given_chrome > p_premium_given_safari:\n",
    "    more_likely_premium = 'Chrome'\n",
    "else:\n",
    "    more_likely_premium = 'Safari'\n",
    "    \n",
    "print(more_likely_premium)    "
   ]
  }
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