6_conditional_probability_hw.ipynb

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    "<font size=\"4\" style=\"color:red;\"> **IMPORTANT: ** When submitting this homework notebook, please modify only the cells that start with:</font>\n",
    "\n",
    "```python\n",
    "# modify this cell\n",
    "```"
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   "source": [
    "# Conditional Probability and Baye's Rule\n"
   ]
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   "source": [
    "## Problem"
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    "There are two urns $A$ and $B$. Urn $A$ contains $r_A$ red balls and $w_A$ white balls whereas urn $B$ contains $r_B$ red balls and $w_B$ white balls. One of the urns is picked at random and then one ball is picked at random from this urn. Write a function **conditional_probability** that calculates the conditional probability that the randomly chosen ball belonged to urn $A$ given that it is white. Assume that $\\frac{r_A}{w_A}\\neq\\frac{r_B}{w_B}$.\n",
    "\n",
    "<font  style=\"color:blue\"> **Code**</font>\n",
    "```python\n",
    "rA, wA, rB, wB = 1., 2., 2., 1.\n",
    "conditional__probability(rA, wA, rB, wB) \n",
    "```\n",
    "\n",
    "<font  style=\"color:magenta\"> **Output**</font>\n",
    "```\n",
    "0.6666666666666666\n",
    "```"
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    "# modify this cell\n",
    "\n",
    "def conditional__probability(rA, wA, rB, wB):\n",
    "    # inputs: all of them are of type 'float'\n",
    "    # output: a variable of type 'float'\n",
    "    \n",
    "    #\n",
    "    # YOUR CODE HERE\n",
    "    Omega = rA+wA+rB+wB\n",
    "    Con_prob = ((rA+wA)/Omega)*(wA/(rA+wA))/((wA+wB)/Omega)\n",
    "    return Con_prob\n",
    "    #\n"
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      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-608ab43f6d0f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mconditional__probability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m2.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.5714285714285715\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mconditional__probability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m5.\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m2.\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m\u001b[1;36m0.7241379310344829\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<\u001b[0m \u001b[1;36m10\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;31m#\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# AUTOGRADER TEST - DO NOT REMOVE\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mAssertionError\u001b[0m: "
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    "assert( abs(conditional__probability(2., 4., 3., 3.) -0.5714285714285715) < 10**-5)  \n",
    "assert( abs(conditional__probability(1., 3., 5., 2.) -0.7241379310344829) < 10**-5) \n",
    "\n",
    "#\n",
    "# AUTOGRADER TEST - DO NOT REMOVE\n",
    "#\n"
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    "\n",
    "conditional__probability(2, 1, 6, 4)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
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