R studio coding problem, Negative Binomial distribution:

Suppose a student has 50% chance of scoring a perfect score in an exam with randomly selected questions. The student has to repeatedly take the exam until they achieve three perfect scores.

a)Compute and plot the probability distribution for scoring the three perfect scores. The student will only go for a maximum of 10 attempts before giving up.

b)What is the probability that the student will have the three perfect scores with exactly 4 failures?

c)What is the probability that the student will have the three perfect scores with at most 4 failures?

d)Repeat a), b) & c) if the student has 75% chance of scoring a perfect score.

e)Repeat a), b) & c) if the student has 25% chance of scoring a perfect score.

f)Simulate the number of failures to get the three perfect scores for 1000 students for the three scenarios above (50%, 75%, 25%). Show the side-by-side barplot of the frequencies of the failures for the three scenarios.