Question

select the correct answer. based on the data in this two - way table, which statement is true? a. p(flower is yellow|flower is rose)≠p(flower is yellow) b. p(flower is hibiscus|color is red)=p(flower is hibiscus) c. p(flower is rose|color is red)=p(flower is red) d. p(flower is hibiscus|color is pink)≠p(flower is hibiscus)

Explanation:

Step1: Recall conditional - probability formula

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

Step2: Analyze option A

$P(\text{flower is yellow}|\text{flower is rose})=\frac{45}{105}=\frac{3}{7}$, $P(\text{flower is yellow})=\frac{135}{315}=\frac{3}{7}$. So $P(\text{flower is yellow}|\text{flower is rose}) = P(\text{flower is yellow})$, option A is false.

Step3: Analyze option B

$P(\text{flower is hibiscus}|\text{color is red})=\frac{80}{120}=\frac{2}{3}$, $P(\text{flower is hibiscus})=\frac{210}{315}=\frac{2}{3}$. So $P(\text{flower is hibiscus}|\text{color is red})=P(\text{flower is hibiscus})$, option B is false.

Step4: Analyze option C

$P(\text{flower is rose}|\text{color is red})=\frac{40}{120}=\frac{1}{3}$, $P(\text{flower is red})=\frac{120}{315}=\frac{8}{21}$. Since $\frac{1}{3}
eq\frac{8}{21}$, $P(\text{flower is rose}|\text{color is red})
eq P(\text{flower is red})$, option C is false.

Step5: Analyze option D

$P(\text{flower is hibiscus}|\text{color is pink})=\frac{40}{60}=\frac{2}{3}$, $P(\text{flower is hibiscus})=\frac{210}{315}=\frac{2}{3}$. So $P(\text{flower is hibiscus}|\text{color is pink}) = P(\text{flower is hibiscus})$, option D is false.

Answer:

None of the above (assuming there is an error in the problem - setup or if we have to choose the most incorrect - among - incorrect - seeming ones, we need to re - check the calculations based on the correct conditional - probability formula). If we assume the question has a correct answer among the given options, we need to re - evaluate the calculations more carefully. But based on the above step - by - step conditional - probability calculations, none of the given statements A, B, C, D are true.