The probability of rain on any given day is 2/3. What is the probability of at most one day of rain during the next three days?

7/27 ≈ 25.9%

Step-by-step explanation:

"At most one" means either exactly 0 or exactly 1.

P (at most 1) = P (0) + P (1)

Using binomial probability:

P (r) = nCr pʳ qⁿ⁻ʳ

P (0) = ₃C₀ (⅔) ⁰ (⅓) ³⁻⁰ = 1/27

P (1) = ₃C₁ (⅔) ¹ (⅓) ³⁻¹ = 2/9

So the probability that it rains on at most one day is:

P (at most 1) = 1/27 + 2/9

P (at most 1) = 7/27

P (at most 1) ≈ 0.259