Definition and basic properties of probability

Axiomatic and classical definitions of probability.

Probability of event. Basic properties of probability.

The axiomatic definition of probability. Let a space of elementary events E be given and such single number Ð ( À ) corresponds to each event À Å , that: Then we say, that the probability is defined on events of E , and the number Ð ( À ) is called the probability of an event A .

The classical definition of probability . Let a space of elementary events E be given and this space consists of N equally likely elementary events, among which there are n events, favorable for an event A . Then the number

Ð ( À ) = n / N

is called the probability of an event A .

Basic properties of probability . Let a space of elementary events E be given and probabilities P are defined on events of E . Then:
{"ft_lang_label":"__label__en","ft_lang_prob":0.9284048,"math_prob":0.99781007,"size":849,"snap":"2022-40-2023-06","text_gpt3_token_len":178,"char_repetition_ratio":0.2,"word_repetition_ratio":0.2628205,"special_character_ratio":0.21672556,"punctuation_ratio":0.10559006,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.999681,"pos_list":[0,1,2,3,4,5,6],"im_url_duplicate_count":[null,null,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-06T09:44:39Z\",\"WARC-Record-ID\":\"<urn:uuid:2ee6b6d1-397d-4e74-9274-c348d10686b0>\",\"Content-Length\":\"12423\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:3b704f91-8a74-4e35-84d1-ff0355e72b34>\",\"WARC-Concurrent-To\":\"<urn:uuid:35451ba6-67d3-41de-8334-fa5a68169394>\",\"WARC-IP-Address\":\"194.233.168.254\",\"WARC-Target-URI\":\"https://bymath.com/studyguide/prob/sec/prob2.php\",\"WARC-Payload-Digest\":\"sha1:V4VB5M7RKZ24Y4Q3YAVFN457SLVM2JJ3\",\"WARC-Block-Digest\":\"sha1:PG7D3GPEQEYZARZP3H3LHMPLZA5CCH2O\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337803.86_warc_CC-MAIN-20221006092601-20221006122601-00190.warc.gz\"}"}