Respuesta :
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
[tex]\begin{gathered} \text{If it was sunny the first day, then we have} \\ \text{SSS, SSR, SRS, SRR} \end{gathered}[/tex][tex]\begin{gathered} \text{If it was rainy the first day, then we have} \\ \text{RRR, RRS, RSR, RSS} \end{gathered}[/tex]So, The total sample space is
[tex]\begin{gathered} S=\mleft\lbrace\text{SSS,SSR,SRS,SR}\R,R\R\R,\text{RRS,RSR,RSS}\mright) \\ n(S)=8 \end{gathered}[/tex]The probability that it is sunny all three days would be
[tex]P(\text{All sunny day)=}\frac{n(all\text{ sunny day)}}{n(Sample\text{ Space)}}[/tex]The Sample space for all sunny day is SSS. so number of element of all sunny day would be
[tex]n(\text{all Sunny day)=1}[/tex]Therefore, the probability that it is sunny all three days would be
[tex]\begin{gathered} P(\text{All sunny day)=}\frac{n(all\text{ sunny day)}}{n(Sample\text{ Space)}} \\ P(\text{All sunny day)=}\frac{1}{8}=0.125 \end{gathered}[/tex]Hence, the probability that it is sunny all three days is 1/8 or 0.125
