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   "source": [
    "# 9.5 - Probability"
   ]
  },
  {
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   "execution_count": null,
   "id": "aefb8b76-b877-4033-bf7d-aeb62ec1cf43",
   "metadata": {},
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97ea4001-440c-4314-95d9-5022c693abb2",
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   "source": [
    "- P(event happens): the probability that an event happens\n",
    "- A probability is in the range [0,1]\n",
    "- P(event happens) = 1 - P(event doesn't happen)\n",
    "- If all events are equally likely, P(event happens) = # outcomes that make event happen / # total outcomes\n",
    "- Multiplication Rule: P(two events happen) = P(one event happens) * P(the other event happens, given that the first one happened)\n",
    "- Addition Rule: P(an event happens) = P(first way it can happen) + P(second way it can happen)\n",
    "- At Least One Success: P(an event occur in n independent trials) = 1 - P(an event doesn't occur in one trial) ^ n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07bdb3eb-9ad1-47aa-8bdd-aa618c519ae8",
   "metadata": {},
   "outputs": [],
   "source": [
    "rolls = np.arange(0, 201, 5)\n",
    "results = Table().with_columns(\n",
    "    'Card Draws', rolls,\n",
    "    'Chance of at least one Spade Ace', 1 - (51/52)**rolls\n",
    ")\n",
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3cfa94e7-b29e-45ae-a716-5b000df604ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "results.scatter('Card Draws')"
   ]
  }
 ],
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