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Finished lab #466

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231 changes: 211 additions & 20 deletions lab-intro-probability.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -38,11 +38,74 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"#code here"
"from scipy.stats import binom"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.8844772466215431\n"
]
}
],
"source": [
"p=0.97 # probability of passengers showing up for the flight\n",
"n=460 # number of tickets (trials)\n",
"distribution = binom(n,p)\n",
"print(distribution.cdf(450)) # the probabillity of hthe chance that there will be enough seats for all 450 passengers"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.11552275337845685\n"
]
}
],
"source": [
"p=0.97 # probability of passengers showing up for the flight\n",
"n=460 # number of tickets (trials)\n",
"distribution = binom(n,p)\n",
"print(1-distribution.cdf(450)) #this is a probability that more than 450 passengers will show up"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability that there are enough seats for all passengers is: 0.8845\n"
]
}
],
"source": [
"p=0.97 # probability of passengers showing up for the flight\n",
"n=460 # number of tickets (trials)\n",
"seats=450\n",
"\n",
"probability = binom.cdf(seats, n, p)\n",
"\n",
"print(f\"The probability that there are enough seats for all passengers is: {probability:.4f}\")\n"
]
},
{
Expand Down Expand Up @@ -70,13 +133,48 @@
"What is the probability that the representative needs to make at least three attempts before successfully resolving a customer complaint?"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.4409999999999998\n"
]
}
],
"source": [
"p=0.3\n",
"n=3\n",
"distribution = binom(n,p)\n",
"print(distribution.pmf(1)) # the probability that at least one of the three attempts will be succsessful is 44%\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.49\n"
]
}
],
"source": [
"#code here"
"import scipy.stats as stats\n",
"p = 0.3 # probability of success on a single attempt\n",
"\n",
"# Calculate the probability of needing at least 3 attempts\n",
"prob_at_least_three_attempts = 1 - stats.geom.cdf(2, p)\n",
"print(prob_at_least_three_attempts)\n",
"\n"
]
},
{
Expand Down Expand Up @@ -111,7 +209,26 @@
"metadata": {},
"outputs": [],
"source": [
"#code here"
"from scipy.stats import poisson"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0129\n"
]
}
],
"source": [
"n=500 # average number of visits per hour\n",
"probability_website_overwelmed = poisson(n).sf(550) # distribution of 550 visits and more - survival function (1 - cdf)\n",
"print(probability_website_overwelmed.round(4)) # probability is 1%"
]
},
{
Expand All @@ -123,11 +240,26 @@
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.2677\n"
]
}
],
"source": [
"#code here"
"n = 500 # average number of visits per hour\n",
"prob_not_overwhelmed_hour = poisson(n).cdf(550) # probability of not being overwhelmed in one hour - at most 550 visits\n",
"\n",
"prob_not_overwhelmed_day = prob_not_overwhelmed_hour ** 24 # probability of not being overwhelmed in all 24 hours\n",
"\n",
"prob_overwhelmed_at_least_once = 1 - prob_not_overwhelmed_day # probability of being overwhelmed at least once during the day\n",
"\n",
"print(prob_overwhelmed_at_least_once.round(4)) # probability is 26%\n"
]
},
{
Expand Down Expand Up @@ -159,8 +291,25 @@
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"data": {
"text/plain": [
"np.float64(0.9925534169290756)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rate_customer_arrives = 1/10\n",
"\n",
"from scipy.stats import expon\n",
"\n",
"expon(rate_customer_arrives).cdf(5) # the probability that customer arrives within next 5 minutes is 99,3%\n"
]
},
{
"cell_type": "markdown",
Expand All @@ -173,10 +322,24 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": []
"outputs": [
{
"data": {
"text/plain": [
"np.float64(3.3807434840493755e-07)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 - expon(rate_customer_arrives).cdf(15)\n",
"\n"
]
},
{
"cell_type": "markdown",
Expand All @@ -196,11 +359,25 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 21,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The probability of the bird's weight is between 140 gr and 160 gr is 0.6826894921370859\n"
]
}
],
"source": [
"#code here"
"from scipy.stats import norm\n",
"\n",
"mean = 150\n",
"std = 10\n",
"\n",
"norm_dist = norm(loc = mean, scale = std)\n",
"print(f\"The probability of the bird's weight is between 140 gr and 160 gr is {norm_dist.cdf(160) - norm_dist.cdf(140)}\")"
]
},
{
Expand All @@ -221,15 +398,29 @@
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.4511883639059735\n"
]
}
],
"source": [
"#code here"
"mean_lifetime = 50\n",
"\n",
"time_for_failure = 30\n",
"\n",
"prob_failure_within_30 = expon.cdf(time_for_failure, scale=mean_lifetime) # probability that the component fails within 30 hours\n",
"\n",
"print(prob_failure_within_30) # 45%\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "base",
"language": "python",
"name": "python3"
},
Expand All @@ -243,7 +434,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
"version": "3.13.5"
}
},
"nbformat": 4,
Expand Down