Let's analyze and solve the questions on your sheet:

Question 1:

The question is asking which sample will likely have the proportion of girls closest to 50% (1/2).

To answer this question, we should choose the sample that is most representative and has the largest number of participants, as larger sample sizes typically yield results that are closer to the actual population proportion.

• Option A: 10 kids in a scout troop – too small to reliably reflect the 1/2 ratio.
• Option B: 25 kids in a middle school math class – better, but still relatively small.
• Option C: 40 kids on a school bus – better than A and B, but still not ideal.
• Option D: 100 kids in the 9th grade – largest sample, more likely to approximate 1/2.

Thus, Option D is the best choice as it provides the largest sample size.

Answer for Question 1: D (A collection of 100 kids in the 9th grade)

Question 2:

The question involves conditional probability. We need to find the probability that a randomly selected college student is a girl, given that the student arrived by car.

Here's how to solve it:

1. Data provided:

   • Total boys surveyed = 220, of which 80 arrive by car.
   • Total girls surveyed = 200, of which 50 arrive by car.

2. Calculate the probability that a student arriving by car is a girl:

   • Total students arriving by car = 80 (boys) + 50 (girls) = 130.
   • The probability that a student arriving by car is a girl = $\frac{\text{girls arriving by car}}{\text{total students arriving by car}}$.

   Substituting values: $P(\text{girl | arrived by car}) = \frac{50}{130} \approx 0.38$

Answer for Question 2: B (0.38)

Would you like more details on these solutions or have any further questions?

Here are some related questions to deepen your understanding:

1. What factors affect the accuracy of proportions in samples?
2. How does sample size influence probability results?
3. What is the general formula for calculating conditional probability?
4. How would the answer change if the sample of students arriving by car increased?
5. How might survey biases affect these types of probability calculations?

Tip: In probability, always double-check whether you're dealing with independent or conditional probabilities to choose the right approach.