Find the probability that a number chosen 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 multiples of 3:
   - Multiples of 3 = $\left\lfloor \frac{300}{3} ightfloor = 100$

3. Count multiples of 7:
   - Multiples of 7 = $\left\lfloor \frac{300}{7} ightfloor = 42$

4. Count multiples of both 3 and 7 (i.e., multiples of 21):
   - Multiples of 21 = $\left\lfloor \frac{300}{21} ightfloor = 14$

5. Using inclusion-exclusion principle, total favorable cases = multiples of 3 + multiples of 7 - multiples of 21
   $$100 + 42 - 14 = 128$$

6. Probability = $\frac{	ext{favorable cases}}{	ext{total cases}} = \frac{128}{300} = \frac{32}{75}$

**Answer:** $\frac{32}{75}$

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