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A students is taking a multiple choice test where each question has 5 possible answers, only one of which is correct. If the student knows the answer he selects the correct answer, otherwise he selects his answer choice randomly. The student knows the answer to $70$% of the questions.

i) What is the probability that on a given question, the student gets the correct answer?

My thought was that I could use conditional probability:

$$\dfrac{(0.2)(0.7)}{0.2}$$

But then thought maybe that would not be appropriate, and a made a tree diagram and came up with an answer of $0.76$. This takes into account, I believe, the cases where he does not know the answer but guesses correctly.

Any thoughts?

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    $\begingroup$ The answer of $.76$ is correct, you can see it as $.7\times 1 +.3\times .2$ $\endgroup$ – lulu Jun 2 '19 at 16:29
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$P($ correct $) = P($ know $)+ ( P $ guesses$)$

$=0.7 \times 1 + 0.3 \times \frac{1}{5}$

Here 0.7 comes from the fact that he knows 70% of material and correctly answers (1)

0.3 comes from fact that he doesn't know 30% of material so he guesses chance of correct guessing is 1 in 5.

Hence required probablilty is $0.76$

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it should be 0.76 . I took 10 questions. He should know 7 and will have a probability of 1/5 for the other three(seperately). The probability for getting correct would be 3/5 . now we add 3/5 and 7 = 7.6 . Now this is the probability for 10 questions. for one it should be 7.6/10= 0.76

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