sara has a box of 12 greeting cards. the cards are equally divided into 3 different designs of butterflies…

sara has a box of 12 greeting cards. the cards are equally divided into 3 different designs of butterflies, shells, and flowers. sara likes all the designs. so, she reaches into the box and randomly selects a card. which three statements are correct? the data does not represent a uniform probability model. each design has the same probability of being randomly selected. the probability of selecting a shell is $\frac{1}{2}$. the probability of selecting a butterfly or shell design is $\frac{1}{3}$. the probability of selecting a butterfly design is $\frac{1}{3}$. the probability of not selecting a flower design is $\frac{2}{3}$.

sara has a box of 12 greeting cards. the cards are equally divided into 3 different designs of butterflies, shells, and flowers. sara likes all the designs. so, she reaches into the box and randomly selects a card. which three statements are correct? the data does not represent a uniform probability model. each design has the same probability of being randomly selected. the probability of selecting a shell is $\frac{1}{2}$. the probability of selecting a butterfly or shell design is $\frac{1}{3}$. the probability of selecting a butterfly design is $\frac{1}{3}$. the probability of not selecting a flower design is $\frac{2}{3}$.

Answer

Explanation:

Step1: Calculate number of cards per design

There are 12 cards divided into 3 designs, so $12\div3 = 4$ cards per design.

Step2: Determine probability of each design

The probability of selecting a card of a particular design is $\frac{4}{12}=\frac{1}{3}$ since there are 4 cards of each design out of 12 total cards. So each design has an equal probability of being selected, which means it is a uniform - probability model.

Step3: Calculate probability of non - flower design

The probability of not selecting a flower design is the probability of selecting a butterfly or shell design. Since the probability of each design is $\frac{1}{3}$, the probability of butterfly or shell is $\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$.

Answer:

B. Each design has the same probability of being randomly selected. E. The probability of selecting a butterfly design is $\frac{1}{3}$. F. The probability of not selecting a flower design is $\frac{2}{3}$.