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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?

Responses
The data does not represent a uniform probability model.
The data does not represent a uniform probability model.
Each design has the same probability of being randomly selected.
Each design has the same probability of being randomly selected.
The probability of selecting a shell is






.
The probability of selecting a shell is 1 half .
The probability of selecting a butterfly or shell design is






.
The probability of selecting a butterfly or shell design is 1 3 .
The probability of selecting a butterfly design is






.
The probability of selecting a butterfly design is 1 3 .
The probability of not selecting a flower design is






.

1 answer

Let's analyze the situation:

  1. Sara has a total of 12 greeting cards divided equally into 3 designs: butterflies, shells, and flowers.

    Therefore, each design has \( \frac{12}{3} = 4 \) cards.

Correct Statements:

  1. Each design has the same probability of being randomly selected.

    • Since there are 3 designs and each design has an equal number of cards (4), the probability of selecting any specific design (butterfly, shell, or flower) is the same.

    \[ P(\text{Butterfly}) = P(\text{Shell}) = P(\text{Flower}) = \frac{4}{12} = \frac{1}{3} \]

  2. The probability of selecting a shell is \( \frac{1}{3} \).

    • As computed above, the probability of selecting a shell card is:

    \[ P(\text{Shell}) = \frac{4}{12} = \frac{1}{3} \]

  3. The probability of selecting a butterfly or shell design is \( \frac{2}{3} \).

    • There are 4 butterfly cards and 4 shell cards, which equals 8 cards for these two designs out of 12.

    \[ P(\text{Butterfly or Shell}) = P(\text{Butterfly}) + P(\text{Shell}) = \frac{4}{12} + \frac{4}{12} = \frac{8}{12} = \frac{2}{3} \]

  4. The probability of not selecting a flower design is \( \frac{2}{3} \).

    • Since there are 4 flower cards, the probability of selecting a flower is \( \frac{4}{12} = \frac{1}{3} \), and therefore, the probability of not selecting a flower design is:

    \[ P(\text{Not Flower}) = 1 - P(\text{Flower}) = 1 - \frac{1}{3} = \frac{2}{3} \]

Incorrect Statements:

  1. The data does not represent a uniform probability model.

    • This statement is incorrect because the probabilities for each design are equal, indicating that it is indeed a uniform probability model.

  2. The probability of selecting a shell is \( \frac{1}{2} \).

    • This statement is incorrect; it should be \( \frac{1}{3} \) as shown above.

  3. The probability of selecting a butterfly design is \( \frac{1}{3} \).

    • This statement is correct.

So the three correct statements are:

  • Each design has the same probability of being randomly selected.
  • The probability of selecting a shell is \( \frac{1}{3} \).
  • The probability of not selecting a flower design is \( \frac{2}{3} \).