have one bag of trail mix. Half the bag contains peanuts, 1/4 of the bag is chocolate candies, and 1/4 of the bag is dried fruit. what is the probability that I will select a chocolate candy A. It is more likely than drawing a piece of dried fruit. B. It is less likely than drawing a piece of dried fruit. C. It is more likely than drawing a peanut. D. It is less likely than drawing a peanut.

To determine the probabilities, let's break down the contents of the bag:

• Peanuts: \( \frac{1}{2} \) of the bag
• Chocolate candies: \( \frac{1}{4} \) of the bag
• Dried fruit: \( \frac{1}{4} \) of the bag

Now we can analyze the probabilities of selecting each type of item:

1. Probability of selecting a chocolate candy: \[ P(\text{Chocolate}) = \frac{1}{4} \]

2. Probability of selecting dried fruit: \[ P(\text{Dried Fruit}) = \frac{1}{4} \]

3. Probability of selecting peanuts: \[ P(\text{Peanuts}) = \frac{1}{2} \]

Now we will compare the probabilities:

• Selecting a chocolate candy (\(P = \frac{1}{4}\)) compared to selecting dried fruit (\(P = \frac{1}{4}\)):

  • \( \frac{1}{4} = \frac{1}{4} \) → They are equally likely.

• Selecting a chocolate candy (\(P = \frac{1}{4}\)) compared to selecting peanuts (\(P = \frac{1}{2}\)):

  • \( \frac{1}{4} < \frac{1}{2} \) → It is less likely to draw a chocolate candy than a peanut.

Based on these comparisons, the correct answers are:

• A. It is more likely than drawing a piece of dried fruit. (No, it's equally likely)
• B. It is less likely than drawing a piece of dried fruit. (No, it's equally likely)
• C. It is more likely than drawing a peanut. (No, it's less likely)
• D. It is less likely than drawing a peanut. (Yes)

Thus, the correct conclusion is D: It is less likely than drawing a peanut.