select the correct answer. based on the data in this two - way table, which statement is true?\n|type of…
select the correct answer. based on the data in this two - way table, which statement is true?\n|type of flower/color|red|pink|yellow|total|\n|----|----|----|----|----|\n|rose|40|20|45|105|\n|hibiscus|80|40|90|210|\n|total|120|60|135|315|\na. a flower being pink and a flower being a rose are independent of each other.\nb. a flower being pink is dependent on a flower being a rose.\nc. a flower being a rose is dependent on a flower being pink.\nd. a flower being pink and a flower being a rose are the same.
Answer
Explanation:
Step1: Calculate probability of a flower being pink
The total number of flowers is 315, and the number of pink - colored flowers is 60. So the probability of a flower being pink, $P(Pink)=\frac{60}{315}=\frac{4}{21}$.
Step2: Calculate probability of a flower being a rose
The total number of flowers is 315, and the number of roses is 105. So the probability of a flower being a rose, $P(Rose)=\frac{105}{315}=\frac{1}{3}$.
Step3: Calculate probability of a flower being pink and a rose
The number of pink roses is 20. So the probability of a flower being pink and a rose, $P(Pink\cap Rose)=\frac{20}{315}=\frac{4}{63}$.
Step4: Check for independence
Two events A and B are independent if $P(A\cap B)=P(A)\times P(B)$. $P(Pink)\times P(Rose)=\frac{4}{21}\times\frac{1}{3}=\frac{4}{63}$ Since $P(Pink\cap Rose) = P(Pink)\times P(Rose)$, a flower being pink and a flower being a rose are independent of each other.
Answer:
A. A flower being pink and a flower being a rose are independent of each other.