Question

The probability of guessing the correct answer to a certain test questions is$$\frac{x}{12}$$ If the probability of not  guessing the correct answer to this question is$$\frac{2}{3}$$ then x = 

Options

• 2

•  3

•  4

• 6

Answer 1

 Probability of guessing a correct answer to a certain question is  ${\displaystyle \frac{x}{12}}$

Probability of not guessing a correct answer to a same question  ${\displaystyle \frac{2}{3}}$

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 ${\displaystyle \overline{E}}$ is its complementary then ${\displaystyle P\left(\overline{E}\right)+P\left(\overline{E}\right)=1}$

According to the question we have 

${\displaystyle \frac{x}{12}+\frac{2}{3}=1}$

${\displaystyle \frac{x+8}{12}=1}$ 

${\displaystyle x+8=12}$

${\displaystyle x=4}$