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

Aa flower being pink and a flower being a rose are independent of each other.
Ba flower being pink is dependent on a flower being a rose.
Ca flower being a rose is dependent on a flower being pink.
Da flower being pink and a flower being a rose are the same.

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

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frika frika · Answer 2 · 2018-08-18T15:04:54-04:00

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.