"rolling a 2 with a die, rolling an odd number with a die"
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Two complementary events have to cover all the possibilities. If you don't get an odd number, do you have to get a 2? Is that the only other possibility?
If you don't get a 2, do you have to get an odd number? Is that the only way to get "not 2"?
Edit: That's a minimum requirement, but not the only one. They have to be mutually exclusive (they can't both happen), and their union has to be the entire space of possibilities.
The probability of 1, 2, or 3 is 0.5 and the probability of 1, 3 or 5 is also 0.5. Their probabilities add up to 1, but they aren't complements. "Not getting a 1, 2, or 3" is not the same as "getting 1, 3, or 5".
Edit: Not vice versa. Getting a 1 and getting a 2 are mutually exclusive, but not complementary. Those possibilities don't cover the whole space.
If you don't get a 2, do you have to get an odd number? Is that the only way to get "not 2"?
Edit: That's a minimum requirement, but not the only one. They have to be mutually exclusive (they can't both happen), and their union has to be the entire space of possibilities.
The probability of 1, 2, or 3 is 0.5 and the probability of 1, 3 or 5 is also 0.5. Their probabilities add up to 1, but they aren't complements. "Not getting a 1, 2, or 3" is not the same as "getting 1, 3, or 5".
Edit: Not vice versa. Getting a 1 and getting a 2 are mutually exclusive, but not complementary. Those possibilities don't cover the whole space.