The probability of rain on each of five days is 1/6, except on the fir

Given data :
Probability of raining on 1st day = \(\frac{2}{5}\)
Probability of raining on other days = \(\frac{1}{6}\)
Probability of raining on 5th day = \(\frac{4}{5}\)

From this we can find probability it didn't rain on
Day 1 = 1 - \(\frac{2}{5}\) = \(\frac{3}{5}\)
Day 2,3,4 = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\)
Day 5 = 1 - \(\frac{4}{5}\) = \(\frac{1}{5}\)

Since we have been asked to find the probability of rain on at least 1 days,
the easiest was is to find the probability that it doesn't rain on either of the days.

P(Raining on at least one day) = 1 - P(Not raining on single day)
= 1 - (\(\frac{3}{5}*\frac{5}{6}*\frac{5}{6}*\frac{5}{6}*\frac{1}{5}\)) = 1 - \(\frac{5}{72} = \frac{67}{72}\)(Option E)