text: # --------------
  import numpy as np
  import pandas as pd
  import matplotlib.pyplot as plt
  
  # code starts here
  df= pd.read_csv(path)
  
  pa=df[df['fico']>700].shape[0]
  
  total=df.shape[0]
  
  p_a=pa/total
  
  df1=df[df['purpose']=='debt_consolidation']
  pb=df[df['purpose']=='debt_consolidation'].shape[0]
  
  p_b= pb/total
  
  p_b
  
  pab=(df[(df['purpose']=='debt_consolidation') & (df['fico']>700)]).shape[0]
  
  p_a_b=pab/total
  
  result=p_a_b==p_a
  print(result)
  
  
  
  
  # code ends here
  
  
  # --------------
  # code starts here
  problp=df[df['paid.back.loan'] == 'Yes'].shape[0]
  
  prob_lp=problp/total
  
  probcs=df[df['credit.policy'] == 'Yes'].shape[0]
  
  prob_cs=probcs/total
  
  prob_pd_cs=0.8323182100683655
  
  new_df=df[df['paid.back.loan'] == 'Yes' ]
  bayes=(prob_pd_cs*prob_lp)/prob_cs
  bayes= np.around(bayes,decimals=4)
  print(bayes)
  
  
  
  # code ends here
  
  
  # --------------
  # code starts here
  import seaborn as sns
  sns.countplot(df['paid.back.loan'])
  plt.show()
  df1 = df[df['paid.back.loan']=='No']
  sns.countplot(df['purpose'][df['paid.back.loan']=='No'])
  plt.show()
  # code ends here
  
  
  # --------------
  # code starts here
  inst_median=df['installment'].median()
  
  inst_mean =df['installment'].mean()
  plt.hist(df['installment'])
  plt.show()
  plt.hist(df['log.annual.inc'])
  plt.show()
  
  
  
  # code ends here
  
  
  