Event (probability theory) Totally Explained

Everything about Event Probability Theory totally explained

In probability theory, an event is a set of outcomes (a subset of the sample space) to which a probability is assigned. Typically, when the sample space is finite, any subset of the sample space is an event (i.e. all elements of the power set of the sample space are defined as events). However, this approach doesn't work well in cases where the sample space is infinite, most notably when the outcome is a real number. So, when defining a probability space it's possible, and often necessary, to exclude certain subsets of the sample space from being events (see §2, below).

A simple example

If we assemble a deck of 52 playing cards and no jokers, and draw a single card from the deck, then the sample space is a 52-element set, as each individual card is a possible outcome. An event, however, is any subset of the sample space, including any single-element set (an elementary event, of which there are 52, representing the 52 possible cards drawn from the deck), the empty set (which is defined to have probability zero) and the entire set of 52 cards, the sample space itself (which is defined to have probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential events include:

"Red and black at the same time without being a joker" (0 elements),
"The 5 of Hearts" (1 element),
"A King" (4 elements),
"A Face card" (12 elements),
"A Spade" (13 elements),
"A Face card or a red suit" (32 elements),
"A card" (52 elements).

Since all events are sets, they're usually written as sets (for example ,

can be written more conveniently as, simply, ť

u < X leq v,.

This is especially common in formulas for a probability, such as ť

P(u < X leq v) = F(v)-F(u),.

Further Information

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