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fix monty hall example
1 parent de03ca3 commit c3809be

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Lines changed: 251 additions & 45 deletions

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‎lec/lec31/monty_hall.ipynb‎

Lines changed: 251 additions & 45 deletions
Original file line numberDiff line numberDiff line change
@@ -2,7 +2,7 @@
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"cells": [
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{
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"cell_type": "code",
5-
"execution_count": null,
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"execution_count": 2,
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"id": "09843234-d9df-4a83-b17c-5eca5d933238",
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"metadata": {},
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"outputs": [],
@@ -26,26 +26,95 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 3,
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"id": "af5a8201-63ae-4b77-9026-196fc7e9d59b",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr>\n",
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" <th>Door</th> <th>Prize</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <td>1 </td> <td>goat 2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>2 </td> <td>goat 1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>3 </td> <td>car </td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>"
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],
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"text/plain": [
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"Door | Prize\n",
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"1 | goat 2\n",
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"2 | goat 1\n",
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"3 | car"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"three_door_prizes = ['car', 'goat 1', 'goat 2']\n",
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"def hide(prizes):\n",
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" prize_table = Table().with_column('Prize', prizes)\n",
3771
" return (prize_table.sample(with_replacement=False)\n",
3872
" .with_column('Door', np.arange(1, len(prizes) + 1))\n",
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" .select('Door', 'Prize'))\n",
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" \n",
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"hide(three_door_prizes)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 4,
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"id": "c9aa84bb-5590-4aed-ac05-fe124e19fa68",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr>\n",
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" <th>Door</th> <th>Prize</th> <th>Status</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <td>1 </td> <td>goat 1</td> <td>Final choice</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>2 </td> <td>goat 2</td> <td>Revealed </td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>3 </td> <td>car </td> <td>Picked first</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>"
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],
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"text/plain": [
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"Door | Prize | Status\n",
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"1 | goat 1 | Final choice\n",
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"2 | goat 2 | Revealed\n",
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"3 | car | Picked first"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"def pick(t):\n",
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" \"\"\"Return the door number of a randomly selected row of a doors table.\"\"\"\n",
@@ -61,30 +130,54 @@
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" what_happened = Table().with_columns(\n",
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" 'Door', [contestant_initial_choice, revealed, contestant_final_choice],\n",
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" 'Status', ['Picked first', 'Revealed', 'Final choice'])\n",
64-
" return doors.join('Door', what_happened, 'Door')"
133+
" return doors.join('Door', what_happened, 'Door')\n",
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"\n",
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"monty_hall()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "93dba6b3-26f3-44e7-a734-c5903b4e1476",
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"execution_count": 5,
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"id": "8630e911-ddfd-4b3b-8d5b-719ee88b2142",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"False"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"monty_hall()"
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"def won_the_car(result_table):\n",
157+
" return result_table.where('Status', 'Final choice').column('Prize').item(0) == 'car'\n",
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"\n",
159+
"won_the_car(monty_hall())"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 6,
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"id": "982c4064-0e60-4818-bc47-ccd68fb2107a",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"66.13 percent cars\n"
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]
174+
}
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],
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"source": [
84177
"trials = 10000\n",
85178
"cars = 0\n",
86179
"for i in np.arange(trials):\n",
87-
" if monty_hall().where('Status', 'Final choice').column('Prize').item(0) == 'car':\n",
180+
" if won_the_car(monty_hall()):\n",
88181
" cars = cars + 1\n",
89182
"print(100 * cars / trials, 'percent cars')"
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]
@@ -99,21 +192,138 @@
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 7,
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"id": "bee4e522-e1d5-4da2-b02c-9f81a732c1b3",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr>\n",
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" <th>Door</th> <th>Prize</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <td>1 </td> <td>goat 1</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>2 </td> <td>goat 2</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>3 </td> <td>car </td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>4 </td> <td>goat 3</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>"
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],
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"text/plain": [
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"Door | Prize\n",
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"1 | goat 1\n",
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"2 | goat 2\n",
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"3 | car\n",
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"4 | goat 3"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"four_door_prizes = ['car', 'goat 1', 'goat 2', 'goat 3']\n",
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"hide(four_door_prizes)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 8,
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"id": "bfa79a80-79d9-44ff-b531-59cf51525129",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"With Lock\n"
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]
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},
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{
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"data": {
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"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr>\n",
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" <th>Door</th> <th>Prize</th> <th>Status</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <td>1 </td> <td>car </td> <td>Locked </td>\n",
267+
" </tr>\n",
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" <tr>\n",
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" <td>2 </td> <td>goat 2</td> <td>Picked first</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <td>3 </td> <td>goat 3</td> <td>Revealed </td>\n",
273+
" </tr>\n",
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" <tr>\n",
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" <td>4 </td> <td>goat 1</td> <td>Final choice</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>"
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],
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"text/plain": [
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"<IPython.core.display.HTML object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Without Lock\n"
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]
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},
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{
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"data": {
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"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
298+
" <thead>\n",
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" <tr>\n",
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" <th>Door</th> <th>Prize</th> <th>Status</th>\n",
301+
" </tr>\n",
302+
" </thead>\n",
303+
" <tbody>\n",
304+
" <tr>\n",
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" <td>1 </td> <td>goat 3</td> <td>Picked first</td>\n",
306+
" </tr>\n",
307+
" <tr>\n",
308+
" <td>2 </td> <td>goat 2</td> <td>Revealed </td>\n",
309+
" </tr>\n",
310+
" <tr>\n",
311+
" <td>3 </td> <td>goat 1</td> <td>Ignored </td>\n",
312+
" </tr>\n",
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" <tr>\n",
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" <td>4 </td> <td>car </td> <td>Final choice</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>"
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],
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"text/plain": [
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"<IPython.core.display.HTML object>"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"def monty_hall_4(lock):\n",
119329
" doors = hide(four_door_prizes)\n",
@@ -141,43 +351,39 @@
141351
" locked, ignored],\n",
142352
" 'Status', ['Picked first', 'Revealed', 'Final choice',\n",
143353
" 'Locked', 'Ignored'])\n",
144-
" return doors.join('Door', what_happened, 'Door')"
145-
]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5ab4f959-6455-4d25-a3ed-ad7a0f545bec",
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"metadata": {},
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"outputs": [],
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"source": [
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"monty_hall_4(True)"
155-
]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f7898c1d-41c9-49ba-b07f-0b5d214f1fed",
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"metadata": {},
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"outputs": [],
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"source": [
164-
"monty_hall_4(False)"
354+
" return doors.join('Door', what_happened, 'Door')\n",
355+
"\n",
356+
"print('With Lock')\n",
357+
"monty_hall_4(True).show()\n",
358+
"print('Without Lock')\n",
359+
"monty_hall_4(False).show()"
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]
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},
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{
168363
"cell_type": "code",
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"execution_count": null,
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"execution_count": 9,
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"id": "fb5f52bf-f6e1-4a9e-8791-b366a9242e70",
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"metadata": {},
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"outputs": [],
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
372+
"With lock equal to True win percentage is 50.26\n",
373+
"With lock equal to False win percentage is 37.79\n"
374+
]
375+
}
376+
],
173377
"source": [
174378
"trials = 10000\n",
175379
"lock = True\n",
176-
"cars = 0\n",
177-
"for i in np.arange(trials):\n",
178-
" if monty_hall_4(lock).where('Status', 'Final choice').column('Prize').item(0) == 'car':\n",
179-
" cars = cars + 1\n",
180-
"print(100 * cars / trials, 'percent cars')"
380+
"\n",
381+
"for lock in [True, False]:\n",
382+
" cars = 0\n",
383+
" for i in np.arange(trials):\n",
384+
" if won_the_car(monty_hall_4(lock)):\n",
385+
" cars = cars + 1\n",
386+
" print('With lock equal to', lock, 'win percentage is', 100 * cars / trials)"
181387
]
182388
}
183389
],

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