1.Experiment<\/strong> :An operation which can produce some well-defined outcome is called an experiment<\/p>\n 2.Random experiment:<\/strong> An experiment in which all possible outcome are known and the exact out put cannot be predicted in advance is called an random experiment<\/p>\n Eg of performing random experiment:<\/strong><\/p>\n (i)rolling an unbiased dice<\/p>\n (ii)tossing a fair coin<\/p>\n (iii)drawing a card from a pack of well shuffled card<\/p>\n (iv)picking up a ball of certain color from a bag containing ball of different colors<\/p>\n (i)when we throw a coin. Then either a head(h)<\/strong> or a tail (t)<\/strong> appears.<\/p>\n (ii)a dice is a solid cube, having 6 faces ,marked 1,2,3,4,5,6 respectively when we throw a die , the outcome is the number that appear on its top face .<\/p>\n (iii)a pack of cards has 52 cards it has 13 cards of each suit ,namely spades,\u00a0 clubs ,hearts and diamonds<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Cards of spades\u00a0 and clubs are black cards<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Cards of hearts\u00a0 and diamonds are red cards<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 There are 4 honors of each suit<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 These are aces ,king ,queen and jack<\/strong><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 These are called face cards<\/p>\n 3.Sample space :W<\/strong>hen we perform an experiment ,then the set S of all\u00a0 possible outcome is called the sample space<\/p>\n eg of sample space:<\/strong><\/p>\n (i)in tossing a coin ,s={h,t}<\/p>\n (ii)if two coin are tossed ,then s={hh,tt,ht,th}.<\/p>\n (iii)in rolling a die we have,s={1,2,3,4,5,6}.<\/p>\n 4.event:A<\/strong>ny subset of a sample space.<\/p>\n 5.Probability of\u00a0 occurrence of an event.<\/strong><\/p>\n let S be the sample space and E be the event .<\/p>\n then,E\u00cdS.<\/p>\n P(E)=n(E)\/n(S).<\/p>\n 6.Results on Probability:<\/strong><\/p>\n (i)P(S) = 1\u00a0 (ii)0<P<\/u>(E)<<\/u>1\u00a0\u00a0\u00a0 (iii)P(f)=0<\/p>\n (iv)For any event\u00a0 a and b, we have:<\/p>\n P(a\u00c8b)=P(a)+P(b)-P(a\u00c8b)<\/p>\n (v)If A denotes (not-a),then P(A)=1-P(A).<\/p>\n Ex 1<\/strong>. In a throw of a coin ,find the probability of getting a head.<\/p>\n sol.<\/strong> Here s={h,t} and e={h}.<\/p>\n P(E)=n(E)\/n(S)=1\/2<\/p>\n Ex2<\/strong>.Two unbiased\u00a0 coin are tossed .what is the probability of getting atmost one head?<\/p>\n sol.H<\/strong>ere s={hh,ht,th,tt}<\/p>\n Let Ee=event of getting one head<\/p>\n e={tt,ht,th}<\/p>\n p(e)=n(e)\/n(s)=3\/4<\/p>\n Ex3.An unbiased die is tossed .find the probability of getting a multiple of 3<\/p>\n sol<\/strong>. Here s={1,2,3,4,5,6}<\/p>\n Let e be the event of getting the multiple of 3<\/p>\n then ,e={3,6}<\/p>\n p(e)=n(e)\/n(s)=2\/6=1\/3<\/p>\n ex4.\u00a0 i<\/strong>n a simultaneous\u00a0 throw of pair of dice .find the probability of getting the total more than 7<\/p>\n sol.<\/strong>\u00a0 Here n(s)=(6*6)=36<\/p>\n let e=event of getting a total more than 7<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}<\/p>\n p(e)=n(e)\/n(s)=15\/36=5\/12.<\/p>\n Ex5.<\/strong> A bag contains 6 white and 4 black balls .2 balls are drawn at random. find the probability that they are of same colour.<\/p>\n Sol<\/strong>\u00a0 .let s be the sample space<\/p>\n Then n(s)=no of ways of drawing 2 balls out of (6+4)=10c2=(10*9)\/(2*1)=45<\/p>\n Let e=event of getting both balls\u00a0 of same colour<\/p>\n Then n(e)=no of ways(2 balls out of six) or(2 balls out of 4)<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =(6<\/sup>c2+4<\/sup>c2)=(6*5)\/(2*1)+(4*3)\/(2*1)=15+6=21<\/p>\n p(e)=n(e)\/n(s)=21\/45=7\/15<\/p>\n Ex6<\/strong>.Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6<\/p>\n sol. <\/strong>Clearly n(s)=6*6=36<\/p>\n Let E be the event that the sum of the numbers on the two faces is divided by 4\u00a0 or 6.Then<\/p>\n e={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),\u00a0\u00a0<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (6,6)}<\/p>\n n(e)=14.<\/p>\n Hence p(e)=n(e)\/n(s)=14\/36=7\/18<\/p>\n Ex7<\/strong>.Two cards are drawn at random from a pack of 52 cards.what is the probability that either both\u00a0 are black or both are queen?<\/p>\n sol. W<\/strong>e have n(s)=52c2=(52*51)\/(2*1)=1326.<\/p>\n Let A=event of getting both black cards<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0 B=event of getting both queens<\/p>\n a\u00c7b=event of getting queen of black cards<\/p>\n n(A)=26<\/sup>c2=(26*25)\/(2*1)=325,<\/p>\n n(b)=4<\/sup>c2=(4*3)\/(2*1)=6 and<\/p>\n n(a\u00c7b)=2c2=1<\/p>\n p(A)=n(A)\/n(S)=325\/1326;<\/p>\n p(B)=n(B)\/n(S)=6\/1326 and<\/p>\n p(a\u00c7b)=n(a\u00c7b)\/n(s)=1\/1326<\/p>\n p(a\u00c8b)=p(a)+p(b)-p(a\u00c7b)=(325+6-1\/1326)=330\/1326=55\/221<\/p>\n RS Aggarwal’s “Quantitative Aptitude for Competitive Examinations” is a widely acclaimed resource for mastering various mathematical concepts, including probability. However, obtaining a free PDF version of this book may infringe upon copyright laws. To ensure ethical use, consider the following options:<\/p>\n Purchase the Book<\/strong>: Acquire a legitimate copy through authorized sellers or online platforms.<\/p>\n<\/li>\n Library Access<\/strong>: Check with local or institutional libraries for availability.<\/p>\n<\/li>\n Official Solutions<\/strong>: For specific chapters like Probability, official solutions are available online. For instance, Vedantu offers free PDF downloads of RS Aggarwal Solutions for Class 12 Maths Chapter 29 – Probability.<\/p>\n<\/li>\n<\/ol>\n By utilizing these resources, you can study probability effectively while respecting intellectual property rights.<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Probability Important Facts and Formula 1.Experiment :An operation which can produce some well-defined outcome is called an experiment 2.Random experiment: An experiment in which all possible outcome are known and the exact out put cannot be predicted in advance is called an random experiment Eg of performing random experiment: (i)rolling an unbiased dice (ii)tossing a […]<\/p>\n","protected":false},"author":41,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[126,127],"tags":[],"class_list":["post-6028","post","type-post","status-publish","format-standard","hentry","category-rs-aggarwal-quantitative-aptitude","category-rs-aggarwal-quantitative-aptitude-pdf"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6028","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/comments?post=6028"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6028\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/media?parent=6028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/categories?post=6028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/tags?post=6028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Details:<\/strong><\/h3>\n
\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SOLVED EXAMPLES<\/strong><\/h2>\n
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RS Aggarwal Quantitative Aptitude PDF Free Download: PROBABILITY<\/h3>\n