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

Explanation:

Step1: Recall the concept of independence

Two events (A) and (B) are independent if (P(A\cap B)=P(A)\times P(B)). Let event (A) be a flower being pink and event (B) be a flower being a rose.

Step2: Calculate probabilities

The probability of a flower being pink (P(\text{pink})=\frac{60 + 20}{315}=\frac{80}{315}=\frac{16}{63}). The probability of a flower being a rose (P(\text{rose})=\frac{40+20 + 45+10}{315}=\frac{115}{315}=\frac{23}{63}). The probability of a flower being pink and a rose (P(\text{pink}\cap\text{rose})=\frac{20}{315}=\frac{4}{63}). And (P(\text{pink})\times P(\text{rose})=\frac{16}{63}\times\frac{23}{63}=\frac{368}{3969}\neq\frac{4}{63}), so they are dependent.

Step3: Analyze each option

• Option A: Since (P(\text{pink}\cap\text{rose})\neq P(\text{pink})\times P(\text{rose})), a flower being pink and a flower being a rose are not independent, so A is false.
• Option B: As calculated above, a flower being pink is dependent on a flower being a rose, so B is true.
• Option C: The correct statement is that a flower being a rose is dependent on a flower being pink, not the other - way - around as stated in a wrong structure in C, so C is false.
• Option D: They are not the same, so D is false.

Answer:

B. A flower being pink is dependent on a flower being a rose.