Bob took a quiz?

Question

Bob took a quiz consisting of 500 questions with two options: Yes and No. Bob did not prepare for the quiz. Flustered, he hastily reached for a fair coin in his wallet and started to toss this coin for answers. Whenever the coin landed heads, he shaded Yes; whenever the coin landed tails, he shaded No. It turned out that 40% of the questions have Yes as the correct answer, and the rest have No as the correct answer. Among those questions that Bob shaded Yes, roughly how many percent did he get correct? A) 30% B) 40% C) 50% D)60% E) 70% My thought is that of the questions he put as Yes, the chance of getting the right answers is equal to 40%. But this is just a guess and I'm not sure of the explanation or if this is the right answer.

Answer 1

One way of looking at the question is to consider the yes and no questions separately. That works because no matter what the question is, he has a 50% marking the question yes. Out of the 500 questions, we marked 250 yes answers.

Since there were 200 yes questions and the student marked about 100 (50%) of those yes, that means that he got about 100 of those correct.

There were 300 no questions and the student marked about 150 (50%) of them with yes answers. He got every one of those 150 questions wrong.

That means that he got 100 questions correct out of the 250 questions that he marked with yes. That comes out to 40 percent.