Question

3 8 of a neighborhood's residents vote to plant roses at the front entrance. 2 9 vote to plant roses and peonies. what fraction of those who vote for roses also vote for peonies?

Answer 1

1627 is correct.
.
P(peonies|roses) = P(roses and peonies)P(roses)
2938 = 1627

Answer 2

Answer: $=\frac{16}{27}$

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=$P(A)=\frac{3}{8}$

The probability of neighborhood's residents vote to plant roses and peonies =$P(A\cap B)=\frac{2}{9}$

Now, the conditional probability of neighborhood's residents vote for roses also vote for peonies =$P(B|A)=\frac{P(A\cap B)}{P(A)}$

$=\frac{\frac{2}{9}}{\frac{3}{8}}\\\\=\frac{2\times8}{9\times3}\\\\=\frac{16}{27}$

Hence, the fraction of neighborhood's residents vote for roses also vote for peonies $=\frac{16}{27}$