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

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$.

Step2: Calculate $P(\text{flower is yellow}|\text{flower is rose})$

$P(\text{flower is yellow}|\text{flower is rose})=\frac{\text{Number of yellow roses}}{\text{Total number of roses}}=\frac{45}{105}=\frac{3}{7}$

Step3: Calculate $P(\text{flower is yellow})$

$P(\text{flower is yellow})=\frac{\text{Total number of yellow flowers}}{\text{Total number of flowers}}=\frac{135}{315}=\frac{3}{7}$

Step4: Analyze option A

Since $P(\text{flower is yellow}|\text{flower is rose}) = P(\text{flower is yellow})$, option A is false.

Step5: Calculate $P(\text{flower is hibiscus}|\text{color is red})$

$P(\text{flower is hibiscus}|\text{color is red})=\frac{\text{Number of red hibiscus}}{\text{Total number of red flowers}}=\frac{80}{120}=\frac{2}{3}$

Step6: Calculate $P(\text{flower is hibiscus})$

$P(\text{flower is hibiscus})=\frac{\text{Total number of hibiscus}}{\text{Total number of flowers}}=\frac{210}{315}=\frac{2}{3}$ Since $P(\text{flower is hibiscus}|\text{color is red}) = P(\text{flower is hibiscus})$, option B is false.

Step7: Calculate $P(\text{flower is rose}|\text{color is red})$

$P(\text{flower is rose}|\text{color is red})=\frac{\text{Number of red roses}}{\text{Total number of red flowers}}=\frac{40}{120}=\frac{1}{3}$ $P(\text{flower is red})=\frac{120}{315}=\frac{8}{21}$ Since $P(\text{flower is rose}|\text{color is red})\neq P(\text{flower is red})$, option C is false.

Step8: Calculate $P(\text{flower is hibiscus}|\text{color is pink})$

$P(\text{flower is hibiscus}|\text{color is pink})=\frac{\text{Number of pink hibiscus}}{\text{Total number of pink flowers}}=\frac{40}{60}=\frac{2}{3}$ $P(\text{flower is hibiscus})=\frac{210}{315}=\frac{2}{3}$ Since $P(\text{flower is hibiscus}|\text{color is pink}) = P(\text{flower is hibiscus})$, option D is true.

Answer:

D. P(flower is hibiscus|color is pink) = P(flower is hibiscus)