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?
+2668 It is easier to count for what we don't what and subtract that from 1.
The probability that there will 0 days of snow is: \({1 \over 2}^3 \times {2 \over 3}^4 = {2 \over 81}\)
Thus, the probability that it will snow for at least 1 day of the week is: \(1 - {2 \over 81} = \color{brown}\boxed{79 \over 81}\)
