Random selection from Pandas groups with equal probability - unexpected behavior

I have 12 unique groups that I am trying to randomly sample, each with a different number of observations. I want to randomly select from the entire population (dataframe), with each group having the same probability of being selected. The simplest example of this would be a data frame with two groups.

    groups  probability
0       a       0.25
1       a       0.25
2       b       0.5

      

        
        
        
      

    

using np.random.choice(df['groups'], p=df['probability'], size=100)

Each iteration will now get a 50% chance to choose group a

and a 50% chance to choosegroup b

To come up with the probabilities, I used the formula:

(1. / num_groups) / size_of_groups

      

        
        
        
      

    

or in Python:

num_groups = len(df['groups'].unique())  # 2
size_of_groups = df.groupby('label').size()  # {a: 2, b: 1}
(1. / num_groups) / size_of_groups

      

        
        
        
      

    

What returns

    groups
a    0.25
b    0.50

      

        
        
        
      

    

This works great until I get 10 unique groups, at which point I start getting weird distros. Here's a small example:

np.random.seed(1234)

group_size = 12
groups = np.arange(group_size)

probs = np.random.uniform(size=group_size)
probs = probs / probs.sum()

g = np.random.choice(groups, size=10000, p=probs)
df = pd.DataFrame({'groups': g})

prob_map = ((1. / len(df['groups'].unique())) / df.groupby('groups').size()).to_dict()

df['probability'] = df['groups'].map(prob_map)

plt.hist(np.random.choice(df['groups'], p=df['probability'], size=10000, replace=True))
plt.xticks(np.arange(group_size))
plt.show()

      

        
        
        
      

    

I would expect a fairly even distribution with a large enough sample size, but I get these wings when the number of groups is 11+. If I change the variable group_size

to 10 or lower, I get the uniform distribution I want.

I can't tell if the problem is with my formula for calculating the probabilities, or perhaps a floating point precision issue? Does anyone know a better way to accomplish this or fix it for this example?

Thanks in advance!