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:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{128}\)
The days are independent, and on each day P(rain) = P(no rain) = \(\frac{1}{2}\).
“Rains only on the first 4 days” means rain on days 1 to 4 and no rain on the other 3 days of the week:
\(\displaystyle P = \left(\frac{1}{2}\right)^4 \times \left(\frac{1}{2}\right)^3\)
\(\displaystyle = \left(\frac{1}{2}\right)^7 = \frac{1}{128}\)
Tip: The word “only” makes the last 3 days dry as well. Leaving out these 3 days gives \(\left(\frac{1}{2}\right)^4 = \frac{1}{16}\), which is Option (3).