Problem Solving

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: ½ D:219/256 E: 15/16

OA D

gmatdriller wrote: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: ½ D:219/256 E: 15/16

OA D

To pass, Brian must correctly answer at least 70% of the 8 questions:
(7/10)(8) = 5.6.
Since the number of correctly answered questions must be an INTEGER VALUE, Brian will pass if he answers correctly at least 6 questions.

P = (good options)/(all possible options).

All possible options:
For each of the 8 questions, there are 2 options: correct or incorrect.
To combine our 2 options for each question, we multiply:
2*2*2*2*2*2*2*2 = 256.

A time-saving tip:
nCr = nC(n-r).

Good options:
From 8 questions, the number of ways to choose 6 to be answered correctly = 8C6 = 8C(8-6) = 8C2 = (8*7)/(2*1) = 28.
From 8 questions, the number of ways to choose 7 to be answered correctly = 8C7 = 8C(8-7) = 8C1 = 8.
From 8 questions, the number of ways to answer all 8 correctly = 1.
Total good options = 28+8+1 = 37.

Resulting probability:
good/all = 37/256.

The correct answer is B.

If the OA is D, then the OA is incorrect.

First there are 2^8 different ways to answer the quiz, or 256.

The ways that the score will be above 75% is if he answers 6, 7, or 8 correctly.

8 is the easy one because there is just 1 solution, all correct. ---- 1

For seven, there are 8 different questions that he could have answered wrong ---- 8

Finally, for 6, you can treat it as arrangements of the letters: TTTTTTFF. This is simply 8!/6!2! = 28.


28 + 8 + 1 = 37

The answer is indeed 37/256

Indeed OA is: B

Thanks all for the contributions

probability is so tricky.


I m able to find than Brian needs to give at least 6 good answers out of 8. & total number of ways = 2^8 = 256

so it can 6,2 OR 7,1 OR 8

but after that totally confused

but now I got another trick
PPPPPPFF OR PPPPPPPF OR PPPPPPPP

8!/6!2! + 8!/7!1! + 8!/8!

28 + 8 + 1 = 37

so 37/256

WHat is wrong with this approach?

P(6 at least)= 1-P(not at least 6)

= 1-P(1 and 2 and 3 and 4 and 5 correct answers)

we have 5 correct answers with P= 1/2*1/2*1/2*1/2*1/2= 1/2^5 = 1/32

1-1/32 = 31/32

Why is my approach wrong?