Question

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.

Answer 1

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.