Here is the definition of mathematical expectation which is also called as frequency or average number of times of occurrence of an event.

Suppose a random experiment is conducted independently 'n' times.
E is an event with probability P,

then out of n times approximate number of times of occurrence of event E is called mathematical expectation or frequency of E.

If the probability of any event E is P, then the frequency of E = n.P

Odds in favor of a event E are defined as P(E) to P(E)

Odds against E are defined as P(E) to P(E)

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