A mixed bag of candy bars that are all the same size contains 14 milk chocolate, 14 dark chocolate, 16 crunch, and 16 white chocolate bars. If two candy bars are randomly selected from the bag without replacement, what is the probability that the first bar is a crunch and the second bar is milk chocolate?

To solve this problem, we'll calculate the probability step by step, taking into account that the candy bars are selected without replacement.

### Step 1: Calculate the total number of candy bars
The bag contains the following candy bars:
- 14 milk chocolate bars
- 14 dark chocolate bars
- 16 crunch bars
- 16 white chocolate bars

The total number of candy bars is:

\[
\text{Total candy bars} = 14 + 14 + 16 + 16 = 60
\]

### Step 2: Probability of selecting a crunch bar first
The probability of selecting a crunch bar first is:

\[
P(\text{First is crunch}) = \frac{\text{Number of crunch bars}}{\text{Total number of candy bars}} = \frac{16}{60} = \frac{4}{15}
\]

### Step 3: Probability of selecting a milk chocolate bar second
After one crunch bar is taken, there are 59 candy bars left, including 14 milk chocolate bars. The probability of selecting a milk chocolate bar second is:

\[
P(\text{Second is milk chocolate} \mid \text{First is crunch}) = \frac{\text{Number of milk chocolate bars}}{\text{Remaining number of candy bars}} = \frac{14}{59}
\]

### Step 4: Calculate the combined probability
Since these two events are dependent (the second selection depends on the first), we multiply the probabilities:

\[
P(\text{First is crunch and second is milk chocolate}) = P(\text{First is crunch}) \times P(\text{Second is milk chocolate} \mid \text{First is crunch})
\]

\[
P(\text{First is crunch and second is milk chocolate}) = \frac{4}{15} \times \frac{14}{59} = \frac{56}{885}
\]

### Final Answer
The probability that the first candy bar is a crunch and the second is a milk chocolate is \( \frac{56}{885} \), which is approximately \( 0.0633 \).

Would you like further clarification, or do you have any other questions?

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Here are 8 related questions you might find interesting:
1. What is the probability that both selected candy bars are crunch bars?
2. What is the probability of selecting a dark chocolate bar first and a white chocolate bar second?
3. How would the probability change if the selection were with replacement?
4. What is the probability of selecting two milk chocolate bars in a row?
5. What is the probability that neither of the selected bars is a crunch bar?
6. What is the probability of selecting a crunch bar first and any chocolate bar (milk, dark, or white) second?
7. How does the probability change if there were 20 milk chocolate bars instead of 14?
8. What is the probability of selecting a milk chocolate or dark chocolate bar in both draws?

**Tip:** When dealing with probabilities without replacement, always remember to adjust the total number of items after each draw.

Explore a probability problem involving the selection of candy bars from a mixed bag. Calculate the probability that the first candy bar is crunch and the second is milk chocolate, considering no replacement. Suitable for advanced high school students.

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