{"id":22079,"date":"2023-06-21T13:03:39","date_gmt":"2023-06-21T07:33:39","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=22079"},"modified":"2023-06-21T17:13:24","modified_gmt":"2023-06-21T11:43:24","slug":"inter-2nd-year-maths-2a-probability-formulas","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/inter-2nd-year-maths-2a-probability-formulas\/","title":{"rendered":"Inter 2nd Year Maths 2A Probability Formulas"},"content":{"rendered":"

Use these Inter 2nd Year Maths 2A Formulas<\/a> PDF Chapter 9 Probability to solve questions creatively.<\/p>\n

Intermediate 2nd Year Maths 2A Probability Formulas<\/h2>\n

\u2192 An experiment that can be repeated any number of times under essentially identical conditions and associated with a set of known results is called a random experiment or trial if the result of any single repetition of the experiment is certain and is any one of the associated set.<\/p>\n

\u2192 A combination of elementary events in a trial is called an event.<\/p>\n

\u2192 The list of all elementary events in a trail is called list of exhaustive events.<\/p>\n

\u2192 Elementary events are said to be equally likely if they have the same chance of happening.<\/p>\n

\"Inter<\/p>\n

\u2192 If there are n exhaustive equally likely elementary events in a trail and m of them are
\nfavourable to an event A, then \\(\\frac{m}{n}\\) is called the probability of A. It is denoted by P(A).<\/p>\n

\u2192 P(A) = \\(\\frac{\\text { Number of favourable cases (outcomes) with respect } A}{\\text { Number of all cases (outcomes) of the experiment }}\\)<\/p>\n

\u2192 The set of all possible outcomes (results) in a trail is called sample space for the trail. It is denoted by ‘S’. The elements of S are called sample points.<\/p>\n

\u2192 Let S be a sample space of a random experiment. Every subset of S is called an event.<\/p>\n

\u2192 Let S be a sample space. The event \u03a6 is called impossible event and the event S is called certain event in S.<\/p>\n

\u2192 Two events A, B in a sample space S are said to be disjoint or mutually exclusive if A \u2229 B = \u03a6<\/p>\n

\u2192 Two events A, B in a sample space S are said to be exhaustive if A \u222a B = S.<\/p>\n

\u2192 Two events A, B in a sample space S are said to be complementary if A \u222a B = S, A \u2229 B = \u03a6. The complement B of A is denoted by A\u0304 (or) Ac<\/sup>.<\/p>\n

\u2192 Let S be a finite sample space. A real valued function P: p(s) \u2192 R is said to be a probability function on S if (i) P(A) \u2265 0 \u2200 A \u2208 p(s) (ii) p(s) = 1<\/p>\n

\u2192 A, B, \u2208 p(s), A \u2229 B = \u03a6 \u21d2 P (A \u222a B) = P(A) + P(B). Then P is called probability function and for each A \u2208 p(s), P(A) is called the probability of A.<\/p>\n

\"Inter<\/p>\n

\u2192 If A is an event in a sample space S, then 0 \u2264 P(A) \u2264 1.<\/p>\n

\u2192 If A is an event in a sample space S, then the ratio P(A) : P\u0304(A\u0304) is called the odds favour to A and P\u0304(A): P(A) is called the odds against to A.<\/p>\n

\u2192 If A, B are two events in a sample space S, then P(A \u222a B) = P(A) + P(B) – P(A \u2229 B)<\/p>\n

\u2192 If A, B are two events in a sample space, then P(B – A) = P(B) – P(A \u2229 B) and P(A – B) = P(A) – P(A \u2229 B) .<\/p>\n

\u2192 If A, B, C are three events in a sample space S, then
\nP(A \u222a B \u222a C) = P(A) + P(B) + P(C) – P(A \u2229 B) – P(B \u2229 C) – P(C \u2229 A) + P(A \u2229 B \u2229 C).<\/p>\n

\u2192 If A, B are two events in a sample space then the event of happening B after the event A happening is called conditional event It is denoted by B\/A.<\/p>\n

\u2192 If A, B are two events in a sample space S and P(A) \u2260 0, then the probability of B after the event A has occured is called conditional probability of B given A. It is denoted by P\\(\\left(\\frac{B}{A}\\right)\\)<\/p>\n

\u2192 If A, B are two events in a sample space S such that P(A) \u2260 o then \\(P\\left(\\frac{B}{A}\\right)=\\frac{n(A \\cap B)}{n(A)}\\)<\/p>\n

\u2192 Let A, B be two events in a sample space S such that P(A) \u2260 0, P(B) \u2260 0, then<\/p>\n