A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.
A)0604
B)1325
C)2000
D)2552
E)8000

Question

Quizplus · Accepted Answer

The probability of guessing one correct answer is 1/5. So, the probability of guessing exactly four correct answers in a row is (1/5)^4. We need to account for all the 30 questions, but only four have to be correct, so we need to multiply by the number of ways of choosing 4 questions out of 30, which is denoted by "30 choose 4" (written as 30C4 or C(30,4)). Therefore, the probability of getting exactly four correct answers is:
(30C4) x (1/5)^4 x (4/5)^26 = 1325 x 0.01024 x 0.002843
= 0.03679 or approximately 0.037
Therefore, the best choice is B) 1325.

A Multiple-Choice Test Has 30 Questions and Each One Has