An exam consists of 8 true/false questions. Brian forgets

BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:04 am

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) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

Answer: B
Source: Veritas Prep

Let's say that you have NO IDEA how to solve this question (many students will face this predicament).

The great thing about probability questions is that, even if you don't know how to answer them, you can often eliminate some answers by using your gut instincts alone.

Brian needs to correctly guess at least 6 of the 8 questions .
How likely does that FEEL?
Well, if you feel the likelihood is less than 50%, then we can eliminate C, D and E.

Great! In 10 seconds, we're down to a 50-50 guess between A and B.

Now, guess A or B and move on knowing that you just added a lot of time to your "time bank" that you can devote to other questions.

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Apr 22, 2020 11:04 am

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) 1/16
B) 37/256
C) 1/2
D) 219/256
E) 15/16

Answer: B
Source: Veritas Prep

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