Question

The probability of guessing the correct answer of a certain test question is ${\displaystyle \frac{x}{12}}$. If the probability of not guessing the correct answer is ${\displaystyle \frac{5}{6}}$ then find the value of x.

Answer 1

Given:

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

Probability of not guessing a correct answer to the same question ${\displaystyle \frac{5}{6}}$

To find:

The value of x = ?

Calculation:

${\displaystyle \frac{x}{12}+\frac{5}{6}=1}$     ...(∵ sum of the probabilities of an even and its complement is) always 1)

${\displaystyle \frac{x}{12}+\frac{10}{12}=1}$

${\displaystyle \frac{x+10}{12}=1}$

x + 10 = 12

x = 12 − 10

x = 2