He probability of rain on any given day is 2/3. What is the probability of at most one day of rain during the next 3 days?
Probability of at most one day of rain during next three day is
At most one day of rain during next three days means rain on not more than one day during next three days.
and P(N N N)=1/3xx1/3xx1/3=1/27#
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To find the probability of at most one day of rain in the next three days, consider the complementary probabilities: zero days of rain and exactly one day of rain.
Let (p) be the probability of rain on any given day, so (p = \frac{2}{3}). The probability of no rain on any given day is (1  p = \frac{1}{3}).

Zero days of rain: The probability of no rain on all three days is ((\frac{1}{3})^3 = \frac{1}{27}).

Exactly one day of rain: The probability of rain on exactly one day out of three can occur in three different ways (rain on the first day, second day, or third day), with no rain on the other two days. The probability for each scenario is (p \times (1p) \times (1p) = \frac{2}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{2}{27}). Since there are three such scenarios, the total probability is (3 \times \frac{2}{27} = \frac{6}{27}).
Adding the probabilities of these two scenarios together gives the total probability of at most one day of rain in the next three days:
[ \text{Total Probability} = \frac{1}{27} + \frac{6}{27} = \frac{7}{27} ]
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