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Complementary events are events that are the complete opposite. The compliment of event A is everything that is not event A.
For example, the complementary event of flipping heads on a coin would be flipping tails.
The complementary event of rolling a 1 or a 2 on a six-sided die would be rolling a 3, 4, 5, or 6.
(The probability of A compliment is equal to 1 minus the probability of A.)
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Probability of an event occurring to the probability that it won't occur?
These events are complementary. Let P(A) = probability event will occur. Then the probability it will not occur is: 1 - P(A).
Are mutually exclusive events also complementary events?
Not necessarily. The probability of a complementary event with probability p is 1-p. Two mutually exclusive events, however, don't necessarily add up to a probability of 1. For example, the probability of drawing a King from a standard deck of cards is 1 in 13, which the complementary probability of not drawing a King is 12 in 13. The probability, however, of drawing a Heart is 1 in 4, while the probability of drawing a Club is also 1 in 4. That leaves Diamonds and Spades, which account for the remaining probability of 2 in 4.
What is the relationship between the probability of a simple event and its complement?
If the probability of an event is p, then the complementary probability is 1-p.
If two events are independent the probability that both occur is?
That probability is the product of the probabilities of the two individual events; for example, if event A has a probability of 50% and event B has a probability of 10%, the probability that both events will happen is 50% x 10% = 5%.
How often is the probability of the complement of an event less than the probability of the event itself?
It depends on the events. The answer is 0.5*(Total number of events - number of events with probability = 0.5) That is, discount all events such that their probability (and that of their complement) is exactly a half. Then half the remaining events will have probabilities that are greater than their complement's.
