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:
`=(16)/(27)`

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)=(3)/(8)`

The probability of neighborhood's residents vote to plant roses and peonies =
`P(A\cap B)=(2)/(9)`

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

`=((2)/(9))/((3)/(8))\\\\=(2*8)/(9*3)\\\\=(16)/(27)`

Hence, the fraction of neighborhood's residents vote for roses also vote for peonies
`=(16)/(27)`