Answer

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Hint: First, we will find the sum of the probabilities of guessing the correct answer and not guessing the correct answer and then take the sum equals to 1. Then we will simplify the obtained equation to the value of \[p\].

Given that the probability of guessing the correct answer is \[\dfrac{p}{{12}}\] and probability of not guessing the correct answer is \[\dfrac{3}{4}\].

We know that the sum of the probability of guessing the correct answer and not guessing the correct answer to the question is 1.

Adding the given probabilities and taking it equals to 1, we get

\[

\Rightarrow \dfrac{p}{{12}} + \dfrac{3}{4} = 1 \\

\Rightarrow \dfrac{{p + 9}}{{12}} = 1 \\

\Rightarrow p + 9 = 12 \\

\Rightarrow p = 12 - 9 \\

\Rightarrow p = 3 \\

\]

Therefore, \[p\] is equal to \[3\].

Hence, the option A is correct.

Note: In this question, the probability of guess a certain question is \[{\text{P}}\left( {\text{E}} \right)\] and probability of not guessing answer is \[{\text{P}}\left( {\overline {\text{E}} } \right)\]. Since \[{\text{P}}\left( {\text{E}} \right) + {\text{P}}\left( {\overline {\text{E}} } \right) = 1\]. Thus, we have taken the sum equals to 1.

__Complete step-by-step solution:__Given that the probability of guessing the correct answer is \[\dfrac{p}{{12}}\] and probability of not guessing the correct answer is \[\dfrac{3}{4}\].

We know that the sum of the probability of guessing the correct answer and not guessing the correct answer to the question is 1.

Adding the given probabilities and taking it equals to 1, we get

\[

\Rightarrow \dfrac{p}{{12}} + \dfrac{3}{4} = 1 \\

\Rightarrow \dfrac{{p + 9}}{{12}} = 1 \\

\Rightarrow p + 9 = 12 \\

\Rightarrow p = 12 - 9 \\

\Rightarrow p = 3 \\

\]

Therefore, \[p\] is equal to \[3\].

Hence, the option A is correct.

Note: In this question, the probability of guess a certain question is \[{\text{P}}\left( {\text{E}} \right)\] and probability of not guessing answer is \[{\text{P}}\left( {\overline {\text{E}} } \right)\]. Since \[{\text{P}}\left( {\text{E}} \right) + {\text{P}}\left( {\overline {\text{E}} } \right) = 1\]. Thus, we have taken the sum equals to 1.

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