text: # --------------
  import numpy as np
  import pandas as pd
  import matplotlib.pyplot as plt
  df=pd.read_csv(path)
  df.head(5)
  p_a=len(df[df.fico > 700])/len(df.fico)
  print(p_a)
  p_b=len(df[df.purpose == 'debt_consolidation'])/len(df.purpose)
  print(p_b)
  df1=df[df.purpose == 'debt_consolidation']
  #df1
  p_a_b=df1[df1['fico'].astype(float) >700].shape[0]/df1.shape[0]
  print(p_a_b)
  result=(p_a_b==p_a)
  print(result)
  
  # code ends here
  
  
  # --------------
  # code starts here
  prob_lp=len(df[df['paid.back.loan']=='Yes'])/df['paid.back.loan'].shape[0]
  prob_cs=len(df[df['credit.policy']== 'Yes'])/df['credit.policy'].shape[0]
  new_df=df[df['paid.back.loan'] == 'Yes']
  prob_pd_cs = new_df[new_df['credit.policy'] == 'Yes'].shape[0] / new_df.shape[0]
  bayes=(prob_pd_cs * prob_lp)/ prob_cs
  print(bayes)
  
  
  
  
  # code ends here
  
  
  # --------------
  # code starts here
  
  
  df['purpose'].value_counts().plot(kind='bar')
  df1=df[df['paid.back.loan']=='No']
  df1['purpose'].value_counts().plot(kind='bar')
  
  
  # code ends here
  
  
  # --------------
  # code starts here
  inst_median=df['installment'].median()
  inst_mean=df['installment'].mean()
  plt.hist(df['installment'])
  plt.hist(df['log.annual.inc'])
  
  
  
  # code ends here
  
  
  