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.

Explanation:

As all the questions of the exam carry 2 points, at least
`(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
`(1)/(2)`.

The probability that exactly n questions will be right is
`^(50)C_n ((1)/(2) )^n ((1)/(2) )^(50 - n) = ^(50)C_n ((1)/(2) )^(50)`.

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

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