\nAn experiment whose outcomes cannot be predicted or determined in advance is called a random experiment.<\/p>\n
Outcome<\/strong> Sample Space<\/strong> Events<\/strong> Types of Events<\/strong> Simple or elementary event:<\/strong> Each outcome of a random experiment is called an elementary event.<\/p>\n Compound events:<\/strong> If an event has more than one outcome is called compound events.<\/p>\n Complementary events:<\/strong> Given an event A, the complement of A is the event consisting of all sample space outcomes that do not correspond to the occurrence of A.<\/p>\n Mutually Exclusive Events<\/strong> Exhaustive Events<\/strong> Mutually Exclusive and Exhaustive Events<\/strong> Probability Function<\/strong> Probability of an Event<\/strong> Addition Rule of Probabilities<\/strong> Note: If A and B are mutually exclusive events, then CBSE Class 11 Maths Notes Chapter 16 Probability Random Experiment An experiment whose outcomes cannot be predicted or determined in […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"\"Get CBSE Class 11 Maths Notes Chapter 16 Probability on Infinity Learn.\"","custom_permalink":"study-material-notes\/class-11\/maths\/probability-class-11-notes-maths-chapter-16\/"},"categories":[92,13,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"\n
\nA possible result of a random experiment is called its outcome.<\/p>\n
\nA sample space is the set of all possible outcomes of an experiment.<\/p>\n
\nAn event is a subset of a sample space associated with a random experiment.<\/p>\n
\nImpossible and sure events:<\/strong> The empty set \u03a6 and the sample space S describes events. Intact \u03a6 is called the impossible event and S i.e. whole sample space is called sure event.<\/p>\n
\nTwo events A and B of a sample space S are mutually exclusive if the occurrence of any one of them excludes the occurrence of the other event. Hence, the two events A and B cannot occur simultaneously and thus P(A \u2229 B) = 0.<\/p>\n
\nIf E1<\/sub>, E2<\/sub>,\u2026\u2026.., En<\/sub> are n events of a sample space S and if E1<\/sub> \u222a E2<\/sub> \u222a E3<\/sub> \u222a\u2026\u2026\u2026. \u222a En<\/sub> = S, then E1<\/sub>, E2<\/sub>,\u2026\u2026\u2026 E3<\/sub> are called exhaustive events.<\/p>\n
\nIf E1<\/sub>, E2<\/sub>,\u2026\u2026 En<\/sub> are n events of a sample space S and if
\nEi<\/sub> \u2229 Ej<\/sub> = \u03a6 for every i \u2260 j i.e. Ei<\/sub> and Ej<\/sub> are pairwise disjoint and E1<\/sub> \u222a E2<\/sub> \u222a E3<\/sub> \u222a\u2026\u2026\u2026. \u222a En<\/sub> = S, then the events
\nE1<\/sub>, E2<\/sub>,\u2026\u2026\u2026, En<\/sub> are called mutually exclusive and exhaustive events.<\/p>\n
\nLet S = (w1<\/sub>, w2<\/sub>,\u2026\u2026 wn<\/sub>) be the sample space associated with a random experiment. Then, a function p which assigns every event A \u2282 S to a unique non-negative real number P(A) is called the probability function.
\nIt follows the axioms hold<\/p>\n\n
\nIf there are n elementary events associated with a random experiment and m of them are favorable to an event A, then the probability of occurrence of A is defined as
\n![\"Probability](\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47896991141_35745c4494_o.png\")
\nThe odd in favour of occurrence of the event A are defined by m : (n \u2013 m).
\nThe odd against the occurrence of A are defined by n \u2013 m : m.
\nThe probability of non-occurrence of A is given by P(\\(\\bar { A }\\)) = 1 \u2013 P(A).<\/p>\n
\nIf A and B are two events associated with a random experiment, then
\nP(A \u222a B) = P(A) + P(B) \u2013 P(A \u2229 B)
\nSimilarly, for three events A, B, and C, we have
\nP(A \u222a B \u222a C) = P(A) + P(B) + P(C) \u2013 P(A \u2229 B) \u2013 P(A \u2229 C) \u2013 P(B \u2229 C) + P(A \u2229 B \u2229 C)<\/p>\n
\nP(A \u222a B) = P(A) + P(B)<\/p>\n<\/h5>\n","protected":false},"excerpt":{"rendered":"