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If an event is absolutely certain to happen is then we say the probability of it happening is 1.
Complementary events are such that one of the events musthappen. Therefore the probability of one of a set of complementary events occurring is 1.
For instance : The probability that a fair coin when tossed will come down showing heads is 1/2, and that it will show tails is also 1/2.
The two events are complementary so the probability that the coin toss will result in either a heads or a tails is 1.
Similarly, the probability that a die when rolled will show a number 1, 2, 3, 4, 5 or 6 is 1 as all six events are complementary.
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What events are such that the occurrence of one does not change the probability of other events?
Independent events.
Two disjoint events in which one or the other must occur are called?
Complements or complementary events
Can independent events exist in reality?
Yes. Independent events can exist in reality. Dependent events means that one event has had an effect on the other. For instance, if we look at the probability of someone going to the shops, and the probability of them buying an apple, the latter is clearly dependent on the former. Independent events are simply events that don't have this connection. The probability of one does not influence or predict the probability of the other. For instance, if I studied the probability of you going to see a film on a particular day, and the probability of someone in China getting a hole in one in golf, these are very clearly independent events.
Is one of two events that are the only ones that can possible happen and sum of whose probabilities is 1?
One of a pair of complementary events.
What does complementarity mean?
"Complementarity" may be "the property of being complementary" or something like that. In geometry, two angles are said to be complementary if their sum is equal to 90 degrees. For example, 30o and 60o are complementary because 30o + 60o = 90o. There are also a number of other applications of the term "complementary" in mathematics. One more might be its use in probability and statistics. If the sum of two probabilities is one, they are said to be complementary. Here's a killer example: On a given coin toss, the probability of a head coming up is complimentary to the probability of a tail coming up. The actual formula is P(A) + P(B) = 1 In a quickie review of probability as it is used here, if something cannot possibly happen, the probability of it happening is zero. If something absolutely will occur without any possibility of anything else happening, the probability of that event happening is one. So probabilities range between zero and one (inclusive). The probability of a head coming up in a coin toss is one 1 in 2, or 50%, or 0.5 (speaking in mathematical terms of probability). The probability of a tail is the same (0.5). Let's just do a quick math thingie with that and get it to lock in: Probability of a head = Ph = 0.5 Probability of a tail = Pt = 0.5 Ph + Pt = 0.5 + 0.5 = 1.0 Ph and Pt are said to be complementary, since Ph + Pt = 1.0
