Rolling of Dice probability of getting exactly two 3s in ‘k’ rolls [closed]

Trying to calculate the probability of getting two 3s in ‘k’ rolls and then bar plot. Prior to me adding the code starting with prob_trials[], it would not return any output. Then when I added the prob_trials[] code, if get the error of tuple not callable.

import random
import pylab

"Calculating probability of getting exactly a 3 in k rolls"

dice=(1,2,3,4,5,6)
one=0
two=0
three=0
four=0
five=0
six=0
for i in range(100):
    result = random.choice(dice)
    if result == 1:
        one +=1
    elif result == 2:
        two +=1
    elif result == 3:
        three +=1
    elif result == 4:
        four +=1
    elif result == 5:
        five +=1 
    elif result == 6:
        six +=1
trial_result = (one, two, three, four, five, six)

prob_trials=[]
for i in range(6):
    a = trial_result(i)/100
    prob_trials.append(a)
    
pltbar(dice,prob_trials)

Answer

I would suggest a direct calculation of the probability. The experiment of rolling a dice getting

1. ‘3’ with probability 1/6
2. ‘not 3’ with probability 5/6

This can be looked as a Bernoulli distribution. Thus, the act of 2 successes in k experiments will be regarded as Binomial distribution. Therefore, the probability of a binomial random variable X to have 2 successes in k attempts will be computed as:

P(X=2) = (k choose 2)*(1/6)^2 * (5/6)^{k-2}

Code example for this will be:

from math import comb

p = 1/6  # probability of success in an experiment
k = 8    # number of experiments, put any number here
s = 2    # number of successes, 2 in our case

prob = comb(k, s) * p**s * (1-p)**(k-s)

print(prob)