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})=(60)/(315)=(4)/(21)`

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

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

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