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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?responsesthe 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 12.the probability of selecting a shell is 1 half .the probability of selecting a butterfly or shell design is 13.the probability of selecting a butterfly or shell design is 1 3 .the probability of selecting a butterfly design is 13.the probability of selecting a butterfly design is 1 3 .the probability of not selecting a flower design is 23.5 cm

1 answer

To analyze the situation with Sara and her 12 greeting cards, we know there are 3 different designs with each design having an equal number of cards. Each design is a butterfly, shell, or flower. Therefore, each design has:

\[ \frac{12 \text{ cards}}{3 \text{ designs}} = 4 \text{ cards per design} \]

Now, let's evaluate the statements one by one:

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

    • This statement is incorrect. The cards are evenly distributed among the three designs, so it does represent a uniform probability model.

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

    • This statement is correct. Each design has an equal probability since there are 4 cards of each type in a total of 12 cards.

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

    • This statement is incorrect. The probability of selecting a shell card is \( \frac{4}{12} = \frac{1}{3} \).

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

    • This statement is incorrect. The probability of selecting a butterfly or shell design is:
      • Probability of selecting a butterfly + Probability of selecting a shell = \( \frac{1}{3} + \frac{1}{3} = \frac{2}{3} \).

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

    • This statement is correct. There are 4 butterfly cards out of 12 total cards, so the probability is \( \frac{4}{12} = \frac{1}{3} \).

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

    • This statement is correct. The probability of selecting a flower design is \( \frac{1}{3} \), so the probability of not selecting a flower design is:
      • 1 - Probability of selecting a flower = \( 1 - \frac{1}{3} = \frac{2}{3} \).

In summary, the three correct statements are:

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