Calculation of probability-
- Experiments and events– The term experiments refer to describe an act which can be repeated under some given conditions. Random experiments are those experiments whose results depend on chance such as tossing of a coin, throwing a dice. The result of a random experiments are called outcomes
- Mutually exclusive events- Two events are said to be mutually exclusive or incompatible when both cannot happen simultaneously in a single trial or the occurrence of any one of them precludes the occurrence of the other. For example if a single coin is tossed either head can be up or tail can be up. Both cannot be up at the same time. These events are called mutually exclusive events. if both cases can be happened then these events are called not mutually exclusive events.
- Independent and dependent events- Two or more events are said to be independent when the outcome of one does not affect and is not affected by other. For example if a coin is tossed twice the result of the second throw would in no way be affected by the result of the first throw. Similarly the results obtained by throwing a dice are independent of the results obtained by drawing an ace from a pack of cards.
- Equally likely events– Events are said to be equally likely when one does not occur more often than the others. For example if an unbiased coin or dice is thrown each face may be expected to be observed approximately the same number of times in the long run, similarly the cards of a pack of playing cards are so closely alike that we expect each card to appear equally often when a large number of drawings are made with replacement. However if the coin or dice is biased we should not expect each face to appear exactly the same number of times.
- Simple and compounds events- In case of simple events we consider the probability of the happening or not happening of single events. For example we might be interested in finding out the probability of drawing a red ball from al bag containing 10 white and 6 red balls. On the other hand in case of compound events we consider the joint occurrence of two or more events.