Richard has been given a 10-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended the class recently, he doesn't know any of the answers. Assuming that Richard guesses on all 10 questions, find the probability that he will answer no more than 2 questions correctly. Round your answer to the nearest thousandth.
A)0.282
B)0.200
C)0.526
D)0.050
E)0.500

Question

Quizplus · Accepted Answer

The probability of guessing one question correctly is 1/4. Since there are 10 questions, the probability of guessing all 10 correctly is (1/4)^10, which is very small. 
To find the probability of guessing no more than 2 questions correctly, we can use the binomial distribution formula:
P(X ≤ 2) = C(10,0) * (1/4)^0 * (3/4)^10 + C(10,1) * (1/4)^1 * (3/4)^9 + C(10,2) * (1/4)^2 * (3/4)^8
where C(n,r) is the combination function.
Using a calculator, we get P(X ≤ 2) ≈ 0.526, rounded to the nearest thousandth. Therefore, the answer is choice C.

Richard Has Been Given a 10-Question Multiple-Choice Quiz in His