Question

Based on the data in this two-way table, which statement is true?
Type of Flower/Color Red Pink Yellow Total
Rose 40 20 45 105
Hibiscus 80 40 90 210
Total 120 60 135 315


A. a flower being pink and a flower being a rose are independent of each other.
B. a flower being pink is dependent on a flower being a rose.
C. a flower being a rose is dependent on a flower being pink.
D. a flower being pink and a flower being a rose are the same.

Answer 1

The question is asking to choose among the following choices that state the fact about the said data in the tables, and according to the given data, I would say that the answer would be letter A. a flower being pink and a flower being a rose are independent of each other. I hope this would help 

Answer 2

If $Pr(A\cap B)=Pr (A)\cdot Pr(B)$, then events A and B are independent, otherwise they are dependent.

Find the probabilities:

1. $Pr(\text{Flower is pink})=\dfrac{60}{315}=\dfrac{4}{21}$

2. $Pr(\text{Flower is rose})=\dfrac{105}{315}=\dfrac{1}{3}$

3. $Pr(\text{Flower is pink}\cap \text{Flower is rose})=\dfrac{20}{315}=\dfrac{4}{63}$.

Now, since $Pr(\text{Flower is pink})\cdot Pr(\text{Flower is rose})=\dfrac{4}{21} \cdot \dfrac{1}{3} =\dfrac{4}{63}=Pr(\text{Flower is pink}\cap \text{Flower is rose})$, you can state that events are independent and correct choice is A.