The question is: A single multiple-choice question has n choices, only one is co

Question

The question is:
A single multiple-choice question has n choices, only one is correct. A student know the answer with probabilty p. If the student knows the answer, he or she guesses randomly. Find the conditional probability that the student knew the answer, given that the question was answered correctly.

I am thinking
A: the question was answered correctly
B1: student knows the answer
B2: student does not know the answer (guess)
P(B1) = ???
P(B2)= 1-p
P(A|B1)= p
P(A|B2)= 1/n

I do not know what the right way of setting them up is but the answer is
(np)/(np+1-p)

Explanation / Answer

Okay sorry I understood the process after looking at it for a while. P(B1) = p (student knows answer with probability p) P(A|B1) = 1 (If the student knows the answer, then the probability of the answer being correct is 1) P(B2) = 1-p (student not knowing answer is P(~B2)) PA|B2) = 1/n (since the guess is random) P(B1|A) = (P(A|B1) P(B1)) / ( P(A|B1)P(B1) + P(A|B2)P(B2) ) P(B1|A) = ( 1*p ) / (1*p + (1/n)(1-p)) (then multiply by n/n) P(B1|A) = (np) / ( np + (n/n)(1-p) P(B1|A) = (np) / (np + 1 - p)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.