Final answer:
To simulate rolling N dice in Python, we define a function called rolldice(N) that uses the random module. To estimate the probabilities of different sums when rolling two dice, we use the function repeatedly and calculate the frequencies of each sum. This is done by rolling the dice a large number of times and dividing the count of each sum by the total number of rolls.
Step-by-step explanation:
To address the question of writing a Python function called rolldice(N) that simulates rolling N dice and returns the sum, we'll define such a function. This function will generate N random numbers between 1 and 6 using Python's random module and return their sum. To estimate the probability distribution of rolling two dice, we can call this function multiple times and tally the results.
Here's an example of Python code for the rolldice function:
import random
def rolldice(N):
return sum(random.randint(1, 6) for _ in range(N))
To estimate the probability distribution for rolling two dice, we would roll the dice a large number of times, say 10,000, and count how often each possible sum appears. Dividing each count by the total number of rolls gives us an estimate of the probability for each sum.
The following code snippet could be used to estimate and print the probability distribution:
from collections import Counter
results = Counter(rolldice(2) for _ in range(10000))
for outcome, count in sorted(results.items()):
print(f'Sum {outcome}: {count/10000:.4f}')
By running the code above, we get an approximation of the probability distribution of the sum of two dice.