Mitchell Marshall
03/20/2023 · Elementary School
\( X \) and \( Y \) are two exhaustive events such that \( P(X)=0,3 \) and \( P(Y)=0,7 \). Prove that \( X \) and \( Y \) are complementary.
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To prove \( X \) and \( Y \) are complementary, we check if their probabilities sum to 1 and if they are mutually exclusive. Given \( P(X) = 0.3 \) and \( P(Y) = 0.7 \), their sum is 1, and since they are exhaustive, they cannot occur together, making them complementary.
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