use R

Hypergeometric distribution

Suppose that your professor created a pool of 60 multiple choice questions and 40 programming questions for the final exam. For each student, a random set of 20 distinct questions from the pool will be presented during the exam. The student has the opinion that the multiple-choice questions are easy to handle than the programming questions.

a) Compute and plot the probability distribution for the number of multiple choice questions out of the 20 questions that the student will be given? b) What is the probability that the student will have exactly 10 multiple choice questions out of the 20 questions in the exam? c) What is the probability that the student will have at least 10 multiple choice questions out of the 20 questions in the exam? d) Simulate the number of multiple choice questions for 1000 students. Show the barplot of the frequencies of the multiple-choice questions.