What is Complementary event?

1.	What is Complementary event?
Answer» Complementary event: The complementary event of A = Event A not happening. Thus, an event and its complementary event are both mutually exclusive and exhaustive. Hence, Probability (event A not happening) = 1 – Probability (event A happening) Thus, P(\(A\)) + P(\(\bar A\)) = 1, where \(\bar A\) denotes the complementary event of A. Ex. Probability of drawing a blue ball from a bag of 4 blue, 6 red and 2 yellow balls = \(\frac{4}{4+6+2}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\) \(\therefore\) P (not drawing a blue ball) = 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)

Answer»

Complementary event: The complementary event of A = Event A not happening. Thus, an event and its complementary event are both mutually exclusive and exhaustive. Hence, Probability (event A not happening) = 1 – Probability (event A happening) Thus, P(\(A\)) + P(\(\bar A\)) = 1, where \(\bar A\) denotes the complementary event of A.

Ex. Probability of drawing a blue ball from a bag of 4 blue, 6 red and 2 yellow balls

= \(\frac{4}{4+6+2}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)

\(\therefore\) P (not drawing a blue ball) = 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)

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