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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def p(i, sample_size, weights):
 """ Given a weighted set and sample size return the probabilty that the weight `i` will be present in the sample. Created to test the output of the `SomeOf` maker class. The math was provided by Andy Blackshaw - thank you dad :) """


        # Determine the initial pick values
        weight_i = weights[i]
        weights_sum = sum(weights)

        # Build a list of weights that don't contain the weight `i`. This list will
        # be used to build the possible picks before weight `i`.
        other_weights = list(weights)
        del other_weights[i]

        # Calculate the probability
        probability_of_i = 0
        for picks in range(0, sample_size):

            # Build the list of possible permutations for this pick in the sample
            permutations = list(itertools.permutations(other_weights, picks))

            # Calculate the probability for this permutation
            permutation_probabilities = []
            for permutation in permutations:

                # Calculate the probability for each pick in the permutation
                pick_probabilities = []
                pick_weight_sum = weights_sum

                for pick in permutation:
                    pick_probabilities.append(pick / pick_weight_sum)

                    # Each time we pick we update the sum of the weight the next
                    # pick is from.
                    pick_weight_sum -= pick

                # Add the probability of picking i as the last pick
                pick_probabilities += [weight_i / pick_weight_sum]

                # Multiply all the probabilities for the permutation together
                permutation_probability = reduce(
                    lambda x, y: x * y, pick_probabilities
                    )
                permutation_probabilities.append(permutation_probability)

            # Add together all the probabilities for all permutations together
            probability_of_i += sum(permutation_probabilities)

        return probability_of_i