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
\(\text{P(A)}\times\text{P(B)}=\text{P(A and B)}\)
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 :-
\(\text{P(Pink)}=\dfrac{60}{315}\)
The total number of roses = 315
Then , the probability of selecting a rose :-
\(\text{P(Rose)}=\dfrac{105}{315}\)
The number of pink roses = 20
Then , the probability of selecting a pink rose :-
\(\text{P(Pink rose)}=\dfrac{20}{315}\)
Now, the product of probabilities of pink flower and roses will be
\(\dfrac{105}{315}\cdot\dfrac{60}{315}=\dfrac{20}{315}\)
i.e. \(\text{P(Pink)}\times\text{P(Rose)}=\text{P(Pink rose)}\)
Therefore, A flower being pink and a flower being a rose are independent of each other.
