Question

You are planning a three day trip to Seattle Washington in October. Use the fact that on each day it could be either sunny or rainy, and that each day is equally likely to be sunny or rainy what is the probability that it is sunny all three days? Type an integer or decimal don’t round

Answer 1

It was stated that there were two possibilities during the day, that is, it can either be a sunny day or a rainy day.

Let us represent a sunny day with S, and represent a rainy day with R.

Using this to get the sample space for the three days as shown below

`\begin{gathered} \text{If it was sunny the first day, then we have} \\ \text{SSS, SSR, SRS, SRR} \end{gathered}`
`\begin{gathered} \text{If it was rainy the first day, then we have} \\ \text{RRR, RRS, RSR, RSS} \end{gathered}`

So, The total sample space is

`\begin{gathered} S=\mleft\lbrace\text{SSS,SSR,SRS,SR}\R,R\R\R,\text{RRS,RSR,RSS}\mright) \\ n(S)=8 \end{gathered}`

The probability that it is sunny all three days would be

`P(\text{All sunny day)=}\frac{n(all\text{ sunny day)}}{n(Sample\text{ Space)}}`

The Sample space for all sunny day is SSS. so number of element of all sunny day would be

`n(\text{all Sunny day)=1}`

Therefore, the probability that it is sunny all three days would be

`\begin{gathered} P(\text{All sunny day)=}\frac{n(all\text{ sunny day)}}{n(Sample\text{ Space)}} \\ P(\text{All sunny day)=}(1)/(8)=0.125 \end{gathered}`

Hence, the probability that it is sunny all three days is 1/8 or 0.125