Important Probability Formulas for JEE and NEET

Things to Remember : Result - 1

(i) SAMPLE – SPACE : The set of all possible outcomes of an experiment is called the SAMPLE–SPACE(S).
(ii) EVENT : A sub set of sample−space is called an EVENT.
(iii) COMPLEMENT OF AN EVENT A : The set of all out comes which are in S but not in A is called the COMPLEMENT OF THE EVENT A DENOTED BY
(iv) COMPOUND EVENT : If  A & B are two given events then A∩B is called COMPOUND  EVENT and is denoted by A∩B or AB or A & B.
(v) MUTUALLY EXCLUSIVE EVENTS : Two events are said to be MUTUALLY EXCLUSIVE (or disjoint or incompatible) if the occurence of one precludes (rules out) the simultaneous occurence of the other. If A & B are two mutually exclusive events then P (A & B) = 0.
(vi) EQUALLY LIKELY EVENTS : Events are said to be EQUALLY LIKELY when each event is as likely to occur as any other event.
(vii) EXHAUSTIVE EVENTS : Events  A,B,C ........ L are said to be  EXHAUSTIVE EVENTS if no  event outside this set can result as an outcome of an experiment . For example, if A & B are two events defined on a sample space S, then A & B are exhaustive  ⇒ A ∪ B = S ⇒ P (A ∪ B) = 1.
(viii) CLASSICAL DEF. OF  PROBABILITY :  If n represents the total  number of equally likely , mutually exclusive and exhaustive outcomes of  an experiment and m of them are  favourable to the  happening  of   the event A, then  the  probability  of happening  of  the  event A is given  by  P(A) = m/n.
Note : (1) 0 ≤  P(A)  ≤ 1
(2)
(3) If x cases are favourable to A &  y cases are favourable to then P(A) = 

  We say that ODDS IN FAVOUR OF A are x : y & odds against A are y : x

RESULT − 2 

AUB = A + B = A or B denotes occurence of at least A or B. For 2 events A & B :