* State whether each of the following statements are true or false. (Que. No. 13 to 16) 13. For an event \( A \), it is possible that \( P(A)=P(\bar{A}) \). 14. The standard form of equation \( y=\frac{1}{2} x \) is \( x-2 y+0=0 \).

Let's evaluate each statement one by one: **13. For an event \( A \), it is possible that \( P(A) = P(\bar{A}) \).** - **Explanation:** In probability theory, for any event \( A \), the probability of the event occurring plus the probability of it not occurring equals 1: \[ P(A) + P(\bar{A}) = 1 \] If \( P(A) = P(\bar{A}) \), then: \[ 2P(A) = 1 \implies P(A) = \frac{1}{2} \] This situation is possible when the event \( A \) is equally likely to occur or not occur, such as flipping a fair coin. - **Conclusion:** **True** --- **14. The standard form of the equation \( y = \frac{1}{2}x \) is \( x - 2y + 0 = 0 \).** - **Explanation:** To convert \( y = \frac{1}{2}x \) to the standard form \( Ax + By + C = 0 \): \[ y = \frac{1}{2}x \implies \frac{1}{2}x - y = 0 \] Multiplying the entire equation by 2 to eliminate the fraction: \[ x - 2y = 0 \] This matches the given standard form \( x - 2y + 0 = 0 \). - **Conclusion:** **True** --- **Summary:** - **Statement 13:** True - **Statement 14:** True