code: def get_p_gender_given_first_name_df() -> pd.DataFrame:
      # We use bayes rule: P(A|B) = P(B|A)*P(A)/P(B)
      p_gender_given_first_name_df = pd.DataFrame(
          index=all_first_names, columns=["male", "female"]
      )
      p_male = 0.5
      p_female = 1 - p_male
      first_names_df = p_gender_given_first_name_df.index.to_frame()
      p_names_given_male = first_names_df.join(
          male_first_names_frequency_df
      )["frequency"]
      p_names_given_female = first_names_df.join(
          female_first_names_frequency_df
      )["frequency"]
      p_first_name = (p_names_given_male * p_male).add(
          p_names_given_female * p_female, fill_value=0
      )
      p_gender_given_first_name_df["male"] = (
          (p_names_given_male * p_male)
          .div(p_first_name, axis=0)
          .fillna(value=0)
      )
      p_gender_given_first_name_df["female"] = (
          (p_names_given_female * p_female)
          .div(p_first_name, axis=0)
          .fillna(value=0)
      )
      return p_gender_given_first_name_df
  
file_path: bias-detector/bias_detector/p_groups_lookup.py
imports: import pandas
  import numpy
  import os
  import sys
label_desc: Use image node_id 3 for calling a global function with example usage: get_p_gender_given_first_name_df() and returns: p_gender_given_first_name_df