MCQ
The probability of guessing the correct answer to a certain test questions is $\frac{\text{x}}{12}$. If the probability of not guessing the correct answer to this question is $\frac{2}{3}$, then $x =$
- A$2$
- B$3$
- ✓$4$
- D$6$
✓
Answer
Correct option: C.
$4$
Given : Probability of guessing a correct answer to a certain question is $\frac{\text{x}}{12}$
Probability of not guessing a correct answer to a same question $\frac{2}{3}$
To find : The value of $x$
Calculation : We know that sum of probability of occurrence of an event and probability of non occurrence of an event is $1$.
If $E$ is an event of occurrence and $\bar{\text{E}}$ is its complementary then
$\text{P(E)}+\text{P}(\bar{\text{E}})=1$
According to the question we have
$\frac{\text{x}}{12}+\frac{2}{3}=1$
$\frac{\text{x}+8}{12}=1$
$\text{x}+8=12$
$\text{x}=4$
Hence the correct option is $c.$
Probability of not guessing a correct answer to a same question $\frac{2}{3}$
To find : The value of $x$
Calculation : We know that sum of probability of occurrence of an event and probability of non occurrence of an event is $1$.
If $E$ is an event of occurrence and $\bar{\text{E}}$ is its complementary then
$\text{P(E)}+\text{P}(\bar{\text{E}})=1$
According to the question we have
$\frac{\text{x}}{12}+\frac{2}{3}=1$
$\frac{\text{x}+8}{12}=1$
$\text{x}+8=12$
$\text{x}=4$
Hence the correct option is $c.$
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