Answer: [tex]=\frac{16}{27}[/tex]
Step-by-step explanation:
Let A be the event of planting rose and B be the event of planting peonies at the front entrance.
Then, The probability of neighborhood's residents vote to plant roses at the front entrance=[tex]P(A)=\frac{3}{8}[/tex]
The probability of neighborhood's residents vote to plant roses and peonies =[tex]P(A\cap B)=\frac{2}{9}[/tex]
Now, the conditional probability of neighborhood's residents vote for roses also vote for peonies =[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{\frac{2}{9}}{\frac{3}{8}}\\\\=\frac{2\times8}{9\times3}\\\\=\frac{16}{27}[/tex]
Hence, the fraction of neighborhood's residents vote for roses also vote for peonies [tex]=\frac{16}{27}[/tex]
