The following contains two pairs of words which are related to each other in a certain way. Three of the following four word-pairs are alike as these have the same relationship and thus form a group. Which word-pair does NOT belong to that group? (The words must be considered as meaningful English words and must not be grouped based on the number of letters/number of consonants/vowels in the word)

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Let's analyze each pair:

1. Joy - Peace: Both are positive emotions or states of mind, often associated with happiness and calmness.
2. Misery - Happiness: These are opposites (antonyms). Misery means great unhappiness, while happiness is a state of being happy.
3. Problem - Concern: Both are negative states or issues that cause worry or require attention. They are related in meaning.
4. Worry - Fear: Both are negative emotions, often associated with anxiety and apprehension. They are related in meaning.

Among the four, only 'Misery - Happiness' is a pair of opposites (antonyms), while the other three pairs are related by similarity or association (synonyms or closely related concepts). Therefore, 'Misery - Happiness' does NOT belong to the group.

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