Question

janet has a box of 30 cards. there are 15 blue cards and 15 green cards in the box. janet pulls out a card, records the color, and returns the card to the box. after pulling out a card 10 times, she which statement describes why/if this result is reasonable?
○ it is reasonable because both 6 and 4 are close to 5.
○ it is reasonable because 6 is more than 4.
○ it is not reasonable because she will always get 5 blue cards and 5 green cards.
○ it is not reasonable because she did not pick enough cards.

Explanation:

1. First, analyze the probability of drawing blue or green cards. Since there are 15 blue and 15 green cards out of 30, the theoretical probability of drawing blue (or green) is $\frac{15}{30} = 0.5$, so we'd expect about 5 blue and 5 green in 10 trials.
2. Now, check the options:

• Option 1: "It is reasonable because both 6 and 4 are close to 5." Since 6 (blue) and 4 (green) are both near the expected 5, this makes sense.
• Option 2: "It is reasonable because 6 is more than 4." The reason for reasonableness isn't about which is more, but about closeness to expectation, so this is wrong.
• Option 3: "It is not reasonable because she will always get 5 blue cards and 5 green cards." Probability doesn't mean certainty; results can vary around the expected value, so this is wrong.
• Option 4: "It is not reasonable because she did not pick enough cards." Even with 10 trials, results close to expectation are reasonable, and the issue isn't the number of trials here but the closeness to the expected value, so this is wrong.

Answer:

A. It is reasonable because both 6 and 4 are close to 5.