{"id":7779,"date":"2017-07-28T10:37:18","date_gmt":"2017-07-28T05:07:18","guid":{"rendered":"http:\/\/race4job.com\/blog\/?p=7779"},"modified":"2017-07-28T10:37:18","modified_gmt":"2017-07-28T05:07:18","slug":"most-important-probability-theory","status":"publish","type":"post","link":"https:\/\/www.race4job.com\/blog\/most-important-probability-theory\/","title":{"rendered":"Most Important Probability Theory"},"content":{"rendered":"

Meaning and definition of Probability<\/span><\/p>\n

As the Oxford dictionary states it, Probability means \u2018The extent to which something is probable; the likelihood of something happening or being the case\u2019.<\/span><\/p>\n

In mathematics too, probability indicates the same \u2013 the likelihood of the occurrence of an event.<\/span><\/p>\n

Basic formula of probability<\/span><\/p>\n

The Probability of the occurrence of an event A is defined as:<\/span><\/p>\n

P(A) = (No. of ways A can occur)\/(Total no. of possible outcomes)<\/span><\/p>\n

Compound probability<\/span><\/p>\n

Compound probability is when the problem statement asks for the likelihood of the occurrence of more than one outcome.<\/span><\/p>\n

Formula for compound probability<\/span><\/p>\n

P(A or B) = P(A) + P(B) \u2013 P(A and B)<\/span><\/p>\n

Experiment:<\/span>
\nAn operation which can produce some well-defined outcomes is called an experiment.<\/span><\/p>\n

Random Experiment:<\/span>
\nAn experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment.<\/span><\/p>\n

Mutually exclusive events:<\/span><\/p>\n

Mutually exclusive events are those where the occurrence of one indicates the non-occurrence of the other<\/span><\/p>\n

OR<\/span><\/p>\n

When two events cannot occur at the same time, they are considered mutually exclusive.<\/span><\/p>\n

Sample Space<\/span><\/p>\n

Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.<\/span><\/p>\n

Examples<\/span><\/p>\n

i) When a coin is tossed, S = {H, T} where H = Head and T = Tail<\/span><\/p>\n

ii) When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}<\/span><\/p>\n

iii) When two coins are tossed, S = {HH, HT, TH, TT} where H = Head and T = Tail<\/span><\/p>\n

Event<\/span><\/p>\n

Any subset of a Sample Space is an event. Events are generally denoted by capital letters A, B , C, D etc.<\/span><\/p>\n

Examples<\/span><\/p>\n

i) When a coin is tossed, outcome of getting head or tail is an event<\/span><\/p>\n

ii) When a die is rolled, outcome of getting 1 or 2 or 3 or 4 or 5 or 6 is an event<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Meaning and definition of Probability As the Oxford dictionary states it, Probability means \u2018The extent to which something is probable; the likelihood of something happening or being the case\u2019. In mathematics too, probability indicates the same \u2013 the likelihood of the occurrence of an event. Basic formula of probability The Probability of the occurrence of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-7779","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/posts\/7779","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/comments?post=7779"}],"version-history":[{"count":1,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/posts\/7779\/revisions"}],"predecessor-version":[{"id":7780,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/posts\/7779\/revisions\/7780"}],"wp:attachment":[{"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/media?parent=7779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/categories?post=7779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.race4job.com\/blog\/wp-json\/wp\/v2\/tags?post=7779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}