Question

Zoe is taking a test with 100 questions. There are 30 True/False questions and 70 multiply-choices questions (4 choices per question). Suppose that she blindly guesses all the questions and the results of the different questions are independent. Approximate the probability that

(a) she answers at least 40 questions correctly.

(b) she gets more correct answers on True/False questions than she does on multiplychoices questions.

Answer 1

Let X denote the number of correct T/F questions and Y denote the number of correct MCQs.

So,

Using Normal approximation,

So, and

a)

Required probability =

b)

Required probability =