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Probability: Definition

Let S be the sample space, then the probability of occurrence of an event E is denoted by P(E) and is defined as
P(E) = 64890.png

When a die is rolled, sample space S = {1, 2, 3, 4, 5, 6}.


Let A = the event of occurrence of an odd number = {1, 3, 5}.


B = the event of occurrence of a number greater than 4 = {5, 6}.


Then P(a) = 64877.png and P(b) = 64871.png.

Complement of an event

Complement of an event E is denoted by E′ or Ec or E′ means non-occurrence of event E. Thus E′ occurs if and only if E does not occur. We have P(E) + P(E′) = 1.

Odds in favor and odds against an event

Let S be the sample space and E be an event. Let E′ denote the complement of event E, then
  1. Odds in favor of event
  2. Odds against an event
Note: Odds in favor of event
E = 65580.png
and odds against event E = 65574.png

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