On each of the first three days of January, there is a 1/2 chance that it will snow where Bob lives. On each of the next four days, there is a 1/3 chance that it will snow. What is the probability that it snows at least once during the first week of January?
+505 We can use complementary counting for this problem by calculating the probability that it will not snow at all first.
That is equal to
\((\frac{1}{2})^3\cdot(\frac{2}{3})^4=\frac{1}{8}\cdot\frac{16}{81}=\frac{2}{81}\)
But we're trying to find the probability that it will snow at least once, so the answer is \(1-\frac{2}{81}=\frac{79}{81}\)
Here's a very similar problem: https://web2.0calc.com/questions/please-help-complementry-probabilty-problem
