Question: A multiple choice exam has 5 questions, with three choices for each question. The passing score is at least four correct answers. (a) What is

A multiple choice exam has 5 questions, with three choices for each question. The passing score is at least four correct answers. (a) What is the probability that a student who answers each question at random passes the test? (b) Assuming a class has 50 students, and all answer each question at random, what is the expected number of students that pass the test?

Solution is attached below but please EXPLAIN how they got the values . thanks !

6. (a) The number of correct answers is Binomial(5, 1/3), so the answer is p = () (3)* (b) The number of students who pass is Binomial(50, p), so the answer is 50p. 2 + (3) (3)

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