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vovikov84 [41]
3 years ago
14

a student either knows the answer or guesses. Let 3434 be the probability that he knows the answer and 1414 be the probability t

hat he guesses. Assuming that a student who guesses at the answer will be correct with probability 1414 . What is the probability that the student knows the answer given that he answered it correctly?
Mathematics
1 answer:
Arlecino [84]3 years ago
6 0

Answer:    \dfrac{12}{13}

Step-by-step explanation:

Let A = he known the answer then A' = he guess the answer.

B = he answered it correctly

As per given , we have

P(A)=\dfrac{3}{4}\ \ ,\ \ P(A')=\dfrac{1}{4}

P(B|A)=1

P(B|A')=\dfrac{1}{4}

By Bayes theorem , we have

P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A')P(A')}\\\\ P(A|B)=\dfrac{1\times\dfrac{3}{4}}{1\times\dfrac{3}{4}+\dfrac{1}{4}\times\dfrac{1}{4}}\\\\= \dfrac{12}{13}

The probability that the student knows the answer given that he answered it correctly is  \dfrac{12}{13} .

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