Find the probability that a randomly selected number from 1 to 300 is divisible by 3 or 7.

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**Solution:**

1. Total numbers from 1 to 300 are 300.

2. Count numbers divisible by 3:
   - Numbers divisible by 3 = $\left\lfloor \frac{300}{3} ightfloor = 100$

3. Count numbers divisible by 7:
   - Numbers divisible by 7 = $\left\lfloor \frac{300}{7} ightfloor = 42$

4. Count numbers divisible by both 3 and 7 (i.e., divisible by 21):
   - Numbers divisible by 21 = $\left\lfloor \frac{300}{21} ightfloor = 14$

5. Using the formula for union of two events:
   $$	ext{Numbers divisible by 3 or 7} = 100 + 42 - 14 = 128$$

6. Probability = $\frac{	ext{Favourable outcomes}}{	ext{Total outcomes}} = \frac{128}{300} = \frac{64}{150} = \frac{32}{75} \approx 0.4267$

7. Among the given options, $\frac{133}{300} \approx 0.4433$ is closest but not exact. Since the exact fraction $\frac{128}{300}$ is not listed, the closest correct option is $\frac{133}{300}$.

**Answer:** $\frac{133}{300}$

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