A box contains 4 chocolates and 1 fruit chew. Clark and Chloe take turns drawing a treat out of the box without replacement. Whoever draws the fruit chew wins. Clark draws first. What is the probability that Chloe wins? Express your answer as a common fraction.

We are asked to find the probability that Chloe wins in a game where Clark and Chloe take turns drawing from a box containing 4 chocolates and 1 fruit chew, without replacement. Clark draws first, and whoever draws the fruit chew wins. 

### Step 1: Total treats in the box
The box contains:
- 4 chocolates
- 1 fruit chew

Thus, there are 5 treats in total.

### Step 2: Possible outcomes
Since there are no replacements, the sequence of draws will continue until all treats are taken. The key to Chloe winning is that Clark must avoid drawing the fruit chew on his first draw, and Chloe must draw it on her turn. Let's examine the possible sequences of draws:

- Clark draws first.
- If Clark draws a chocolate, Chloe gets her turn.
- If Chloe does not draw the fruit chew either, Clark gets another turn, and so on.

To find the probability that Chloe wins, we must calculate the chance that the fruit chew appears on Chloe's turn.

### Step 3: Probability breakdown
Let’s consider the turn structure:
- **Clark's first turn**: He must not draw the fruit chew, so the probability of this is \(\frac{4}{5}\), since 4 of the 5 treats are chocolates.
- **Chloe's first turn**: The box now contains 4 treats, 3 chocolates and 1 fruit chew. Chloe wins if she draws the fruit chew, so the probability is \(\frac{1}{4}\).

Thus, the probability that Chloe wins on her first turn is:
\[
P(\text{Chloe wins on her first turn}) = \frac{4}{5} \times \frac{1}{4} = \frac{4}{20} = \frac{1}{5}
\]

### Step 4: Conclusion
The probability that Chloe wins the game is \( \frac{1}{5} \).

Would you like more details or have any other questions? 

Here are 5 related questions to consider:
1. What is the probability that Clark wins?
2. What is the probability that the game lasts more than two turns?
3. How does the probability change if there were 3 chocolates instead of 4?
4. What is the expected number of turns in this game?
5. How would the solution change if the fruit chew were replaced after each draw?

**Tip:** When calculating probabilities, think of breaking down complex events into sequential steps and calculate the likelihood of each step.

Find out how to calculate the probability that Chloe wins in a sequential drawing game involving chocolates and a fruit chew. This problem covers core probability concepts, sequential events, and basic probability theorems. Suitable for students in Grades 6-8.

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