def remove_elderly_non_hospitalised(df, age_range, prob_remove=0.5):
    """
    Remove some fraction (prob_remove) of people in a given age range 
    who weren't admitted to hospital
    
    Parameters
    ==========
    df: pandas DataFrame
    age_range: list of 2 ints, min and max of age range to be removed
    prob_remove (optional): fraction of patients within age range to remove
    """
    query_string = "({} < age < {}) & (admitted==False)".format(age_range[0], age_range[1])
    df_new = df.drop(df.query(query_string).sample(frac=prob_remove).index)
    return df_new