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)
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