Question

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?

Answer 1

7/27 ≈ 25.9%

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