Step 1
The total probability of event happening + event not happening = 1
Assuming the order of rain does not matter there are 6 possibilities;
[tex]0,1,2,3,4,5[/tex]The probability being asked for is if the number of days is at least 1. That is;
[tex]1,2,3,4,5[/tex]Therefore, we can find the probability of no rain happening. That is 0. Then subtract it from 100%.
The probability of no rain happening for 1 day is
[tex]1-0.2=0.8[/tex]So the probability of rain not happening everyday is;
[tex]0.8^5=\frac{1024}{3125}[/tex]Therefore, the probability of rain happening at least once is;
[tex]\begin{gathered} Pr(rain\text{ at least once\rparen=1-}\frac{1024}{3125}=1-0.32768=0.67232 \\ Pr(rain\text{ at least once\rparen}\approx\text{0.672 to 3 decimal places} \end{gathered}[/tex]Answer;
[tex]0.672[/tex]