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Sunless in Seattle - Answer

The probability of the sun shining on at least 4 out of 5 days is 11/243.

The probability of 5 sunny days is (1/3)[superscript 5] = 1/243.

The probability of 1 cloudy day and 4 sunny days is (2/3) (1/3)4[superscript 4] = 2/243. There are 5 ways this can occur.

The probability of sun on at least 4 out of 5 days is then 1/243 + 5(2/243) = 11/243.