Split an amount into 2 random groups by Gauss bell

Let's suppose I've 100 items and I need to split them into two groups.

Options can be:

1. Divide by 2, so I get exactly 50 and 50

2. Select a random number between 1 and 100 and then separate that amount from the rest.

In option 2, 1 item has the same probability than 50 items (1/100)
But in the reality, I imagine a Gauss bell where for e.g., 50 has the most probability, 49 and 48 the less, 47 and 46 more less, and so far.

Question:

How can simulate that "random with probability" selection?
Is there any function to do this in .NET 6?

By the way I'm working in C# but I think I can handle the lines, so that's why I don't write code here, but not the logic.

Thanks in advance

You can achieve your option 2 by iterating through the set of items and allocating each one to set 1 or set 2 with probability p = 0.5. The resulting sets have a binomial distribution, B(n=100, p=0.5), which will give a discrete approximation to the bell-shaped normal distribution. The actual results will vary, but there's a low likelihood of the set counts varying from 50 by more than 10, which corresponds to 2 standard deviations with that parameterization.

I'm not a C# user so I won't attempt to fake it in your preferred language, but it's pretty straightforward. Since Python is widely used and is pseudocode-like, here's the algorithm in that language:

import random

# create an array with the numbers 1 to 100
values = [i for i in range(1, 101)]

# repeat the following set of operations 10 times...
for replication in range(10):
    # create two empty arrays
	set1 = []
	set2 = []

    # Note: random.random() produces float values in the range [0.0, 1.0),
    # the probability of getting a value < 0.5 is 1/2

    # iterate through each of the values from the array created above
	for value in values:
		if random.random() < 0.5:  # with probability 1/2
			set1.append(value)     # the value goes in the first set
		else:
			set2.append(value)     # otherwise it goes in the second set

    # once all values have been allocated, count how
    # many are in each set and print the results
	print(len(set1), " : ", len(set2))

which produces 10 splits such as:

49  :  51
48  :  52
47  :  53
59  :  41
39  :  61
50  :  50
43  :  57
54  :  46
50  :  50
60  :  40

If you want to favor one set or the other, adjust the p-value for the allocations. By simply changing the conditional to

if random.random() < 0.7:

you'll get results such as:

71  :  29
76  :  24
80  :  20
67  :  33
67  :  33
72  :  28
66  :  34
67  :  33
72  :  28
68  :  32