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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?

 Apr 14, 2022
 #1
avatar+1384 
+1

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: \(1 - {2 \over 81} = \color{brown}\boxed{79 \over 81}\)

 Apr 14, 2022
 #2
avatar+326 
+1

Why are there so many counting and prob questions today????

Vinculum  Apr 14, 2022

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