Answer: A: A flower being pink and a flower being a rose are independent of each other.
Step-by-step explanation:
We know that if event A and B are independent then
[tex]\text{P(A)}\times\text{P(B)}=\text{P(A and B)}[/tex]
From the given table we have ,
The number of pink flower = 60
Total number of roses = 315
Then ,the probability of selecting a pink flower :-
[tex]\text{P(Pink)}=\dfrac{60}{315}[/tex]
The total number of roses = 315
Then , the probability of selecting a rose :-
[tex]\text{P(Rose)}=\dfrac{105}{315}[/tex]
The number of pink roses = 20
Then , the probability of selecting a pink rose :-
[tex]\text{P(Pink rose)}=\dfrac{20}{315}[/tex]
Now, the product of probabilities of pink flower and roses will be
[tex]\dfrac{105}{315}\cdot\dfrac{60}{315}=\dfrac{20}{315}[/tex]
i.e. [tex]\text{P(Pink)}\times\text{P(Rose)}=\text{P(Pink rose)}[/tex]
Therefore, A flower being pink and a flower being a rose are independent of each other.
