GMAT Quantitative Reasoning Practice Test 1

Question : 79 of 100

Marks: +1, -0

9 If a person randomly guesses on each question of a test with n questions, what is the probability of guessing half of the questions correctly if each question has five possible answer choices?

$5^n$
$(5 \/ 2)^n$
$(1 \/ 5)^{2 n}$
$(1 \/ 5)^{n \/ 2}$
$(1 \/ 5)^n$

Validate

Solution:

If you are randomly guessing with five possible answer choices, the probability of guessing correct is 1 out of 5, or

1/5

. Since the test has n number of questions and we want to get half of them correct, we want this to happen

n/2

times. Therefore, the probability would be

1 / 5

times itself

n / 2

times, or

(1 / 5)^{n / 2}

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