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16 July, 09:37

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?

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  1. 16 July, 09:42
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    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
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