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[lab-intro-prob] Valeriya Tolmacheva #210

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214 changes: 190 additions & 24 deletions your-code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -19,12 +19,38 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 21,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"'\\nChecking if events are independent:\\nFor independent events, P(A∩B) = P(A) * P(B). 0.1 is not equal to 0.3 multiplied by 0.6, so these events are dependent\\n\\n1) P(A U B) = P(A) + P(B) - P(A∩B) = 0.8, not 0.6, so statement is false\\n2) P(A∩Bcompl) is all of A minus intersection of B and A => P(A) - P(A∩B) = 0.3 - 0.1 = 0.2, so statement is true\\n3) B U Bcompl is full sample, so A ∩ with full sample is just A. P(A) = 0.3, so statement is false\\n4) A compl intersect with B compl is all of sample minus A joined with B => 1 - P(A U B) => 1 - 0.8 = 0.2, so statement is false\\n5) P(not(A∩B)) = 1 - P(A∩B) = 0.9, so statement is true\\n\\n\\n1st statement is false\\n2nd statement is true\\n3rd statement is false\\n4th statement is false\\n5th statement is true\\n\\n'"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
"your solution here\n",
"Checking if events are independent:\n",
"For independent events, P(A∩B) = P(A) * P(B). 0.1 is not equal to 0.3 multiplied by 0.6, so these events are dependent\n",
"\n",
"1) P(A U B) = P(A) + P(B) - P(A∩B) = 0.8, not 0.6, so statement is false\n",
"2) P(A∩Bcompl) is all of A minus intersection of B and A => P(A) - P(A∩B) = 0.3 - 0.1 = 0.2, so statement is true\n",
"3) B U Bcompl is full sample, so A ∩ with full sample is just A. P(A) = 0.3, so statement is false\n",
"4) A compl intersect with B compl is all of sample minus A joined with B => 1 - P(A U B) => 1 - 0.8 = 0.2, so statement is false\n",
"5) P(not(A∩B)) = 1 - P(A∩B) = 0.9, so statement is true\n",
"\n",
"\n",
"1st statement is false\n",
"2nd statement is true\n",
"3rd statement is false\n",
"4th statement is false\n",
"5th statement is true\n",
"\n",
"\"\"\""
]
},
Expand All @@ -43,14 +69,17 @@
]
},
{
"cell_type": "code",
"execution_count": null,
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": [
"\"\"\"\n",
"your solution here\n",
"\"\"\""
"*1) Taking white ball out <br>\n",
"P(W) = 10 / 30 = 1/3=0.33 <br>\n",
"2) Taking white ball out after taking a black ball out<br>\n",
"P(W) = 10/29 =0.345 <br>\n",
"3) Taking red ball out after taking a black ball and a red ball out<br>\n",
"P(R) = 11/28 =0.393 <br>\n",
"4) Taking red ball out after taking a black ball and a red ball out with reposition<br>\n",
"P(R) = 12/30 =0.4 <br>*"
]
},
{
Expand All @@ -69,14 +98,18 @@
]
},
{
"cell_type": "code",
"execution_count": null,
"cell_type": "markdown",
"metadata": {},
"outputs": [],
"source": [
"\"\"\"\n",
"your solution here\n",
"\"\"\""
"R - rainy<br>\n",
"C - cloudy<br>\n",
"P(C|R) = 0.5<br>\n",
"P(C) = 0.4<br>\n",
"P(R) = 3/30 = 0.1<br>\n",
"P(C|R) != P(C), so events are dependent<br>\n",
"**Find**: P(R|C).\n",
"<br><br>\n",
"P(R|C) = P(C|R) * P(R) / P(C) = 0.5 * 0.1 / 0.4 = 0.125\n"
]
},
{
Expand All @@ -102,22 +135,155 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 6,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>yes</th>\n",
" <th>no</th>\n",
" <th>total</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>men</th>\n",
" <td>324</td>\n",
" <td>156</td>\n",
" <td>480</td>\n",
" </tr>\n",
" <tr>\n",
" <th>women</th>\n",
" <td>351</td>\n",
" <td>169</td>\n",
" <td>520</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" yes no total\n",
"men 324 156 480\n",
"women 351 169 520"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# your code here"
"import pandas as pd\n",
"dict={\"men\":{\"yes\":324,\"no\":156,\"total\":480},\"women\":{\"yes\":351,\"no\":169,\"total\":520}}\n",
"df=pd.DataFrame.from_dict(dict,orient=\"index\")\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 10,
"metadata": {},
"outputs": [],
"outputs": [
{
"data": {
"text/plain": [
"0.675"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\"\"\"\n",
"your solution here\n",
"\"\"\""
"#Probability of answer being a yes = sum(yes)/sum(total)\n",
"prob_yes=df[\"yes\"].sum()/df[\"total\"].sum()\n",
"prob_yes"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.48"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Probability of responder being a man = sum(total men)/sum(total)\n",
"prob_men=df.loc[\"men\",\"total\"]/df[\"total\"].sum()\n",
"prob_men"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.324"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#intersection of these two events is when men have answered yes:\n",
"prob_intersect=df.loc[\"men\",\"yes\"]/df[\"total\"].sum()\n",
"prob_intersect"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Events are independent\n"
]
}
],
"source": [
"#For independent events, P(A∩B)=P(A)*P(B)\n",
"if prob_intersect == prob_yes * prob_men:\n",
" print(\"Events are independent\")\n",
"else:\n",
" print(\"Events are dependent\") "
]
}
],
Expand All @@ -137,7 +303,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.2"
"version": "3.11.4"
}
},
"nbformat": 4,
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