The types of events in probability are independent, mutually exclusive or conditional (solve more Conditional Probability Problems here). An event means set of one or more outcomes.
Let us take an example. We throw a die. E1 is an event to get a perfect square number. Then E1 = 2, 4. Suppose that 3 comes up on the upper face, then this means that the event E1 has not occurred. Event occurs only when 2 or 4 appears on the upper face. Therefore, if an outcome satisfies the conditions, then we say that the event has occurred. If z is the outcome and E1 is the event of a sample space S’ and then event E1 has occurred if z belongs to E1.
In mutually exclusive two events associated with a random experiment, if both the events cannot occur together in the same trial. In the above experiment of throwing a die, the events A = 2, 4 and B = 1, 5, 6 are mutually exclusive events and in the same experiment, the events A = 2, 3, 4, and C = 2, 4, 5, 6 are not mutually exclusive because 2 and 4 appears on both events A and C. From this the definition of mutually exclusive events can extended to more than two events. If the happening of one rules out of these then we can say that more than two events are mutually exclusive. An events A = 1, 4, B = 2 and C= 5, are mutually exclusive with the experiment of throwing a single die.
Let A and B are two events, then A or B or (A ∪ B) represented the event of the occurrence of at least one of the events A or B. A and B or (A ∩ B) shows the event of the occurrence of both events A and B. If A and B happen to be mutually exclusive then events can be written as P (A ∩B) = 0. This is the type of events in probability for Grade XI.
Let us take an example. We throw a die. E1 is an event to get a perfect square number. Then E1 = 2, 4. Suppose that 3 comes up on the upper face, then this means that the event E1 has not occurred. Event occurs only when 2 or 4 appears on the upper face. Therefore, if an outcome satisfies the conditions, then we say that the event has occurred. If z is the outcome and E1 is the event of a sample space S’ and then event E1 has occurred if z belongs to E1.
In mutually exclusive two events associated with a random experiment, if both the events cannot occur together in the same trial. In the above experiment of throwing a die, the events A = 2, 4 and B = 1, 5, 6 are mutually exclusive events and in the same experiment, the events A = 2, 3, 4, and C = 2, 4, 5, 6 are not mutually exclusive because 2 and 4 appears on both events A and C. From this the definition of mutually exclusive events can extended to more than two events. If the happening of one rules out of these then we can say that more than two events are mutually exclusive. An events A = 1, 4, B = 2 and C= 5, are mutually exclusive with the experiment of throwing a single die.
Let A and B are two events, then A or B or (A ∪ B) represented the event of the occurrence of at least one of the events A or B. A and B or (A ∩ B) shows the event of the occurrence of both events A and B. If A and B happen to be mutually exclusive then events can be written as P (A ∩B) = 0. This is the type of events in probability for Grade XI.
In upcoming posts we will discuss about Measures of dispersions in Grade XI and circles. Visit our website for information on CBSE previous year question papers class 12
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