Question

50 question true-false final exam (two-points each question) and you never paid attention in the class (or knew anything about the topic on your own), what is probability you will receive a grade of 56 or less, in which case you will fail the class? What is the probability you will get at least 30 questions right, which will give you a passing grade in the class?

Answer 1

Title:

Check the explanation.

Step-by-step explanation:

As all the questions of the exam carry 2 points, at least $\frac{56}{2} = 28$ questions need to be correct to get 56 marks.

In order to get a maximum of 56 marks, at most 28 answers needs to be correct.

Every question has two option. Hence, the probability of getting a particular question right is $\frac{1}{2}$.

The probability that exactly n questions will be right is $^{50}C_n (\frac{1}{2} )^n (\frac{1}{2} )^{50 - n} = ^{50}C_n (\frac{1}{2} )^{50}$.

The probability that at most 28 questions will be right is ∑$^{50}C_n (\frac{1}{2} )^{50}$, $0\leq n\leq 28$.

Similarly, the probability that at least 30 questions will be right is ∑$^{50}C_n (\frac{1}{2} )^{50}$, $30\leq n \leq 50$.