The probability that it will rain on any particular day is 50%. The probability that it rains only on the first 4 days of the week is:

$\frac{1}{128}$

The correct answer is Option (2) → $\frac{1}{128}$

$\text{Probability of rain on a day} = \frac{1}{2}$

$\text{Probability of no rain on a day} = \frac{1}{2}$

$\text{To rain only on the first 4 days and not on last 3:}$

$= \left(\frac{1}{2}\right)^4 \cdot \left(\frac{1}{2}\right)^3 = \left(\frac{1}{2}\right)^7 = \frac{1}{128}$