Question

select the correct answer.
based on the data in this two - way table, which statement is true?

type of flower/color	red	pink	yellow	total
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.

Explanation:

Step1: Define independence rule

Two events \(A\) and \(B\) are independent if \(P(A \cap B) = P(A) \times P(B)\)

Step2: Calculate \(P(\text{Rose} \cap \text{Pink})\)

\(P(\text{Rose} \cap \text{Pink}) = \frac{20}{315} = \frac{4}{63}\)

Step3: Calculate \(P(\text{Rose})\)

\(P(\text{Rose}) = \frac{105}{315} = \frac{1}{3}\)

Step4: Calculate \(P(\text{Pink})\)

\(P(\text{Pink}) = \frac{60}{315} = \frac{4}{21}\)

Step5: Verify independence

\(P(\text{Rose}) \times P(\text{Pink}) = \frac{1}{3} \times \frac{4}{21} = \frac{4}{63}\)
This equals \(P(\text{Rose} \cap \text{Pink})\), so the events are independent.

Answer:

A. A flower being pink and a flower being a rose are independent of each other.