* 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 $$ x-2 y+0=0 $$.

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UpStudy AI · Accepted Answer

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
- **Statement 13:** True - **Statement 14:** True

State whether each of the following statements are true or false.
(Que. No. 13 to 16)

For an event , it is possible that .

The standard form of equation is .

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State whether each of the following statements are true or false. (Que. No. 13 to 16) For an event , it is possible that . The standard form of equation is .