Can Anyone explain how to solve this question? I am preparing for the GRE

Suppose a teacher gives an exam with 10 problems each worth 10 points, and a student knows the answer to each problem independently with a 90% probability.

a) What is the expected score of the student?

b) What is the probability the student gets an A (i.e., >= 90%)?

Now suppose the teacher instead decides to give an extra 11th problem, but the student only chooses 10 to solve. For simplicity, assume that if the student knows the answer, the student is 100% confident in his or her answer.

c) Under this new scheme, what is the probability the student gets an A (i.e., >= 90%)?

d) Under this new scheme, what is the expected score of the student?

Guest Aug 26, 2017