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To find the probability that Jodie wins one event and loses the other, we need to consider the two scenarios where this happens:
1. Jodie wins the 100m freestyle and loses the 50m butterfly.
2. Jodie loses the 100m freestyle and wins the 50m butterfly.

From the tree diagram:
- The probability that Jodie wins the 100m freestyle and then loses the 50m butterfly:
  - Probability of winning the 100m freestyle = 0.6
  - Probability of losing the 50m butterfly given she won the 100m freestyle = 0.8
  - Combined probability = \( 0.6 \times 0.8 = 0.48 \)

- The probability that Jodie loses the 100m freestyle and then wins the 50m butterfly:
  - Probability of losing the 100m freestyle = 0.4
  - Probability of winning the 50m butterfly given she lost the 100m freestyle = 0.2
  - Combined probability = \( 0.4 \times 0.2 = 0.08 \)

Now, add these two probabilities to get the total probability that Jodie wins one event and loses the other:
\[ 0.48 + 0.08 = 0.56 \]

So, the probability that Jodie wins one event and loses the other is **0.56**.

Do you want more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the probability that Jodie wins both events?
2. What is the probability that Jodie loses both events?
3. How would the probabilities change if the probability of winning the 50m butterfly after losing the 100m freestyle was different?
4. What is the probability that Jodie wins at least one event?
5. If Jodie were to compete in three events, how would we set up the probability tree diagram?

**Tip:** When solving probability problems involving multiple events, drawing a tree diagram helps visualize all possible outcomes and simplifies the process of calculating the probabilities.

What is the probability that Jodie wins one event and loses the other?

Learn how to calculate the probability that Jodie wins one event and loses the other using tree diagrams. This problem involves calculating probabilities of independent events and applying the multiplication rule of probability. Suitable for Grades 9-10 students studying probability.

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