Question

The probability of getting a correct answer to a question is \(\frac{x}{12}\). If the probability of not getting the correct answer is \(\frac{2}{3}\), then what is the value of x ?

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The Correct Option is C

To solve the problem, we need to find the value of \(x\) given the probability of getting a correct answer, \(P(C)\), and the probability of not getting a correct answer, \(P(NC)\). We know that the sum of probabilities for all possible outcomes must equal 1. Therefore, we have:

\[ P(C) + P(NC) = 1 \]

Given \(P(C)=\frac{x}{12}\) and \(P(NC)=\frac{2}{3}\), substitute these values into the equation:

\[ \frac{x}{12} + \frac{2}{3} = 1 \]

To solve for \(x\), first convert \(\frac{2}{3}\) to a fraction with a denominator of 12, which is the same as the denominator of \(\frac{x}{12}\):

\[ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \]

Now substitute this value back into the equation:

\[ \frac{x}{12} + \frac{8}{12} = 1 \]

Combine the fractions on the left side:

\[ \frac{x+8}{12} = 1 \]

To eliminate the fraction, multiply both sides by 12:

\[ x+8 = 12 \]

Subtract 8 from both sides to solve for \(x\):

\[ x = 12 - 8 \]

\[ x = 4 \]

Thus, the value of \(x\) is 4.