CUET UG 2025 — Mathematics Arithmetic

The question asks for the probability that it rains only on the first 4 days of the week.

This means it must rain on Monday, Tuesday, Wednesday, and Thursday, and must not rain on Friday, Saturday, and Sunday.

---

The probability of rain on any day is $\frac{1}{2}$21​.

The probability of no rain on any day is $\frac{1}{2}$21​.

---

Since each day's weather is independent, the probabilities are multiplied.

For the first 4 days (rain required):
Probability $= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \left(\frac{1}{2}\right)^4$=21​×21​×21​×21​=(21​)4

For the remaining 3 days (no rain required):
Probability $= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \left(\frac{1}{2}\right)^3$=21​×21​×21​=(21​)3

---

Total Probability $= \left(\frac{1}{2}\right)^4 \times \left(\frac{1}{2}\right)^3$=(21​)4×(21​)3

$$= \left(\frac{1}{2}\right)^7$$=(21​)7

$$= \frac{1}{128}$$=1281​

Therefore, the probability that it rains only on the first 4 days of the week is $\frac{1}{128}$1281​.