ch1 notes update

reading/000_Introduction to Probability, Statistics, and Random Processes/ch1/notes.ipynb

@@ -55,7 +55,14 @@
     "$n = 3$ case:\n",
     "\n",
     "$|A \\cup B \\cup C| = |A| + |B| + |C| - |A \\cap B| - |A \\cap C| - |B \\cap C| + |A \\cap B \\cap C|$\n",
-    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c7475d4f",
+   "metadata": {},
+   "source": [
     "## Random experiments (1.3.1 - 1.4)\n",
     "\n",
     "- A **random experiment** is a process by which we observe something uncertain\n",
@@ -80,13 +87,25 @@
     "\n",
     "\\begin{align*}\n",
     "P(A) = \\frac{|A|}{|S|}\n",
-    "\\end{align*}\n",
+    "\\end{align*}"
-    "\n",
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b705ef32",
+   "metadata": {},
+   "source": [
     "## Conditional probability (1.4.0)\n",
     "\n",
     "If $A$ and $B$ are twos events in sample space $S$, then the **conditional probability of $A$ given $B$** is defined as\n",
     "\n",
     "\\begin{align*}\n",
+    "P(A|B) = \\frac{P(A \\cap B)}{P(B)}, \\text{when } P(B) > 0\n",
+    "\\end{align*}\n",
+    "\n",
+    "or\n",
+    "\n",
+    "\\begin{align*}\n",
     "P(A|B) = \\frac{|A \\cap B|}{|B|}, \\text{when } P(B) > 0\n",
     "\\end{align*}\n",
     "\n",