Question

Use the "at least once" rule to find the probability of the following event.Getting rain at least once in 5 days if the probability of rain on each single day is 0.2. Round to 3 decimal places

Answer 1

Step 1

The total probability of event happening + event not happening = 1

Assuming the order of rain does not matter there are 6 possibilities;

`0,1,2,3,4,5`

The probability being asked for is if the number of days is at least 1. That is;

`1,2,3,4,5`

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

`1-0.2=0.8`

So the probability of rain not happening everyday is;

`0.8^5=(1024)/(3125)`

Therefore, the probability of rain happening at least once is;

`\begin{gathered} Pr(rain\text{ at least once\rparen=1-}(1024)/(3125)=1-0.32768=0.67232 \\ Pr(rain\text{ at least once\rparen}\approx\text{0.672 to 3 decimal places} \end{gathered}`

Answer;

`0.672`