Question - Based on given Python Code so it can do the Following Task (Will Probably have to use Matplotlib): a. Utilizing the code and the output it provides. Create a bar graph that compares the probabilities of the 7 Most Common Numbers with the probabilities of those 7 most common numbers winning the Powerball. | ** An example of how the bar graph should look is shown in the other attached picture (Note that "Testament" is referring to the original number list given in the code called number_lists. Current output of the code: Most Common Numbers in New Testament: Number 21 appears 17 times Number 25 appears 14 times Number 18 appears 14 times Number 20 appears 9 times Number 17 appears 8 times Number 27 appears 8 times Number 31 appears 8 times Least Common Numbers in New Testament: Number 8 appears 1 times Number 12 appears 1 times Number 60 appears 1 times Number 57 appears 1 times Number 62 appears 1 times Number 49 appears 1 times Number 80 appears 1 times Probabilities of 7 Most Common Numbers (Using Binomial Distribution): Probability of seeing 21 appear exactly 17 times: 0.0996 Probability of seeing 25 appear exactly 14 times: 0.1090 Probability of seeing 18 appear exactly 14 times: 0.1090 Probability of seeing 20 appear exactly 9 times: 0.1341 Probability of seeing 17 appear exactly 8 times: 0.1418 Probability of seeing 27 appear exactly 8 times: 0.1418 Probability of seeing 31 appear exactly 8 times: 0.1418 Probabilities of 7 Most Common Numbers from the New Testament Winning the Powerball: Probability of Number 17 being a winning number for Powerball: 0.0200 Probability of Number 18 being a winning number for Powerball: 0.0400 Probability of Number 20 being a winning number for Powerball: 0.0400 Probability of Number 21 being a winning number for Powerball: 0.0800 Probability of Number 25 being a winning number for Powerball: 0.0200 Probability of Number 27 being a winning number is 0 because it is not a Powerball number. Probability of Number 31 being a winning number is because it is not a Powerball number. Press any key to continue Probability 0.10 0.08 0.06 0.04 0.02 0.00 Poisson Distribution Curve Poisson Distributions for Testament and Powerball Probabilities Testament Probabili Powerball Probabilit 10 15 20 Numbers 25 30
Edit the given Python Code (about Probability) so it can also Output a Bar Graph. Please see the attached pics to complete it. Note: The provided Bar Example Picture shows a curve that was done in Poisson Distribution, the code I provided uses Binomial so make sure that the graph shows Binomial Dist.
Code that Needs to be Edited:
from collections import Counter
from scipy.stats import binom
# Part A: Find the 7 most common repetitive numbers
number_list = [25, 23, 17, 25, 48, 34, 29, 34, 38, 42, 30, 50, 58, 36, 39, 28, 27, 35, 30, 34, 46, 46, 39, 51, 46, 75,
66, 20, 45, 28, 35, 41, 43, 56, 37, 38, 50, 52, 33, 44, 37, 72, 47, 20, 80, 52, 38, 44, 39, 49, 50, 56,
62, 42, 54, 59, 35, 35, 32, 31, 37, 43, 48, 47, 38, 71, 56, 53, 51, 25, 36, 54, 47, 71, 53, 59, 41, 42,
57, 50, 38, 31, 27, 33, 26, 40, 42, 31, 25, 26, 47, 26, 37, 42, 15, 60, 40, 43, 48, 30, 25, 52, 28, 41,
40, 34, 28, 40, 38, 40, 30, 35, 27, 27, 32, 44, 31, 32, 29, 31, 25, 21, 23, 25, 39, 33, 21, 36, 21, 14,
23, 33, 27, 31, 16, 23, 21, 13, 20, 40, 13, 27, 33, 34, 31, 13, 40, 58, 24, 24, 17, 18, 18, 21, 18, 16,
24, 15, 18, 33, 21, 13, 24, 21, 29, 31, 26, 18, 23, 22, 21, 32, 33, 24, 30, 30, 21, 23, 29, 23, 25, 18,
10, 20, 13, 18, 28, 12, 17, 18, 20, 15, 16, 16, 25, 21, 18, 26, 17, 22, 16, 15, 15, 25, 14, 18, 19, 16,
14, 20, 28, 13, 28, 39, 40, 29, 25, 27, 26, 18, 17, 20, 25, 25, 22, 19, 14, 21, 22, 18, 10, 29, 24, 21,
21, 13, 15, 25, 20, 29, 22, 11, 14, 17, 17, 13, 21, 11, 19, 17, 18, 20, 8, 21, 18, 24, 21, 15, 27, 21]
number_count = Counter(number_list)
most_common = number_count.most_common(7)
print("Most Common Numbers in New Testament:")
for num, count in most_common:
print(f"Number {num} appears {count} times")
# Part B: Find the 7 most uncommon numbers
least_common = number_count.most_common()[:-8:-1]
print("\nLeast Common Numbers in New Testament:")
for num, count in least_common:
print(f"Number {num} appears {count} times")
# Part C: Use binomial distribution to find the probability of each of the 7 common repetitive numbers
print("\nProbabilities of 7 Most Common Numbers (Using Binomial Distribution):")
for num, count in most_common:
total_trials = len(number_list)
successes = count
probability = binom.pmf(successes, total_trials, successes/total_trials)
print(f"Probability of seeing {num} appear exactly {count} times: {probability:.4f}")
print("\nProbabilities of 7 Most Common Numbers from the New Testament Winning the Powerball:")
# The provided "how often" data from the table
how_often_data = {
1: 4, 2: 4, 3: 3, 4: 7, 5: 8, 6: 4, 7: 3, 8: 4, 9: 6, 10: 3,
11: 2, 12: 3, 13: 3, 14: 5, 15: 2, 16: 5, 17: 2, 18: 4, 19: 3,
20: 4, 21: 8, 22: 1, 23: 5, 24: 1, 25: 2, 26: 4
}
# The total count of all occurrences
total_count = sum(how_often_data.values())
# The specific numbers we need to find the probabilities for
requested_numbers = [17, 18, 20, 21, 25, 27, 31]
# Calculate the probabilities
probabilities = {number: how_often_data.get(number, 0) / total_count for number in requested_numbers}
def print_probability(number, probability):
if number in how_often_data:
print(f"Probability of Number {number} being a winning number for Powerball: {probability:.4f}")
else:
print(f"Probability of Number {number} being a winning number is 0 because it is not a Powerball number.")
for number in requested_numbers:
print_probability(number, probabilities[number])
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