Problem Solving

M7MBA wrote: ↑

Thu Oct 29, 2020 12:28 pm

An exam consists of \(8\) true/false questions. Brian forgets to study, so he must guess blindly on each question. If any score above \(70\%\) is a passing grade, what is the probability that Brian passes?

A) \(\dfrac1{16}\)

B) \(\dfrac{37}{256}\)

C) \(\dfrac12\)

D) \(\dfrac{219}{256}\)

E) \(\dfrac{15}{16}\)

Answer: B

Solution:

Since 70% of 8 is 5.6, Brian must answer at least 6 questions correctly in order to pass the exam.

The probability that he answers exactly 6 questions correctly is:

8C6 x (1/2)^6 x (1/2)^2 = 28 x (1/2)^8 = 28/256

The probability that he answers exactly 7 questions correctly is:

8C7 x (1/2)^7 x (1/2)^1 = 8 x (1/2)^8 = 8/256

The probability that he answers all 8 questions correctly is:

8C8 x (1/2)^8 x (1/2)^0 = 1 x (1/2)^8 = 1/256

Therefore, the probability that he answers at least 6 questions correctly is:

28/256 + 8/256 + 1/256 = 37/256

Answer: B