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25, Probability, , INTRODUCTION, as:, statements such, , In, , come across, everyday life, we, will rain today., (i) Most probably it, will go up., that the prices of petrol, ii) Chances a r e high, will win the race., the, (ii) I doubt that he, etc., show, , The words, , 'most probably',, , probability, , or, , occurrence, , of, , 'chances, 'doubt',, , an event., , outcomes, , well-defined, , some, , c a n produce, An operation which, event., is called a n, outcome, experiment. Each, , is called aan, n, , EXPERIMENT, , outcomes are, , which all possible, An experiment in, called, advance, is, be predicted in, , RANDOM EXPERIMENT, , cannot, exact outcome, , Thus, when, , we, , throw a, , coin, , we, , know that all, , at random,, But, if we throw a coin, show a head or a tail., , face will, , Performing, , a random, , we, , possible, , cannot, , predict, , referred, experiment is often, , random, , a, , outcomes are, , in, , as a, , known, , and the, , experimen., , head and, , advance whether, , tail., , its upDer, , trial., , THEIR OUTCOMES, SOME EXPERIMENTS AND, I. TOSSINGA COIN:, , Suppose, , we, , toss a coin and let it, , fall flat, , on, , the, , ground., , show either Head, Its upper face will, , (H), , or Tail (T)., Whatever, , a n outcome., up, is called, and Tail (T)., outcomes a r e Head (H), , comes, , All possible, , I1. TOSSING TWO COINS:, , Suppose we, , toss two coins, , Here HH means Head, HT, , means, , Head, , on, on, , outcomes, simultaneously. Then, all possible, , 1st coin and Head, 1st coin and Tail, , on, , on, , are, , HH. HT, TH and TT., , 2nd coin,, , 2nd coin,, , etc.|, , II. THROWING A DIE:, , A die is, , a, , Suppose, , is dice., solid cube having 6 faces, marked as 1, 2, 3, 4,5, 6 respectively. Plural of die, on the ground. Then, its upper face will show one of the, we throw a die and let it fall, , numbers 1, 2, 3, 4, 5 and 6., , Whatever number comes up, is called an outcome., All possible outcomes are 1, 2, 3, 4, 5, 6., 278

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279, , Probability, CARD FROM A WELL-SHUFFLED DECK OF, 52 CARDS:, , pAAWINGA CARD, , cards has in all 52 cards., , playing, k of, of each of 4 suits, namely, 13, cards, , ades, clubs, hearts and diamonds., , s, , p, , a, , d, , e, , s, , ,, , ards of spades and clubs are black cards., rts and diamonds are red, (1) Cards ofi, cards., (i), , Car, , Spades, , Clubs, , Hearts, , Diamonds, , 16S, queens and jacks (or knaves) are known as face cards., Thus, t h e r e a r e, , in all 12 face cards., , King, , Queen, , Jack, , SUMMARY, 1. In tossing a coin, all possible outcomes are H, T., , tossing 2 coins,, , 2. In, , all, , possible outcomes are HH, HT., , TH. TT, , 3. On rolling a die, all possible outcomes are 1, 2. 3, 4. 5. 6, number of, 4. In drawing a card from a well-shuffled deck of 52 cards,, all possible outcomes is 52., , EVENT, , of some, , The collection, , EXAMPLES, , or, , all possible outcomes is called, , event., , an, , I. In throwing a coin:, , (i) His the event of getting a head;, (ii) T is the event of getting a tail., II. In, , throwing, , two coins, , simultaneously:, , is the event of getting head, head, HT is the event of getting, , (i) HH, (ii), , (ii) TH, , (iv), , on, , each coin;, , on, , 1st coin and tail, , on, , 2nd coin:, , head, , on, , 2nd coin:, , getting tail o n 1st coin and, of getting tail on each coin., , is the event of, , TT is the event, , III. In rolling a die:, , (i)gettinga, (ii) getting, (iii) getting, , number, say 4, is, , a n even, an, , number is, , odd number is, , an, an, , an, , event;, event E, , event F, , containing 2, 4, 6:, containing 1, 3, 5., , PROBABILITY OF OCCURRENCE OF AN EVENT, D e an, , event., , of o c c u r r e n c e of E is defined, Then, the probability, number offavourable outcomes, P(E) =, , total number, , of outcomes, , as

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Mathematics for Class 8, , EXAMPLE 1., , SOLVED EXAMPLES, , The, , figure shows sptnning wheel divtded into, eightadjoining, sectors. Three, of these sect, ectors are painted red and the, emaining five are painted, , white,, What is the, Spinned., (ti) red, probability of, a, , Solution, , sector?, Total number of, (1) Number of sectors 8., white sectors, , shown. The wheel is, getting () a white sector?, , R, , as, , R, , N, , =, , N, , W, , 5., , =, , Plgetting a white sector) 5=, (i1) Number of, red sectors, A, , Solution, , n, , coin is, , 8, , tossed. What, , is the, , probability of getting a, , tossinga coin, all possible outcomes are H and T., total, , Number, , number, , of heads, , Plgetting a, , Solution, , 3., , Plgettinga red sector) =, , EXAMPLE 2., , EXAMPLE 3., , 8, =, , of all, , possible outcomes, , =, , head?, , 2., , 1., , =, , head), , =, , *2, , When 2 coins are, tossed, what are all possible, Single throw of 2 coins, simultaneously,, outcomes? In, what, is the, (ii) at least 1 head1?, probability of getting () both heads?a, When two coins, , TH, TT., , are, , tossed, , simultaneously,, , total number of all, possible outcomes, (i) Getting both heads, means HH., , Number of such outcomes, , Plgetting, , =, , all, , possible, , outcomes, , are, , HH,, , HT, , 4., , =1., , both heads)=, , 1, 4, , (ii), , Getting at least 1 head means HT, TH, HH., Number of such outcomes 3., =, , Plgetting at least 1 head) = 3, 4, , EXAMPLE 4., , There are 35 students in a class,, of whom 20 are boys and 15 are, these students, one is chosen at random., girls. From, What is the, that, the chosen, probability, student is a (i) boy? (ii) girl?, , Solution, , Total number of students, =35, (i) Let the chosen student be a, , Number of boys, , =, , boy., , 20, , 20, Plchoosing a boy) = ", , 4, , 35, , 7, , (ii) Let the chosen student be, , a, , girl., , Number of girls = 15., , Pfchoostng a girl), , =, , 15 3, 357

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281, , Probability, ELAMPLE5, , one ball is, A bag contains 6 red and 8 green balls. They are mixed thoroughly and, ball., drawn at random. Find the probability of getting (i) a red ball, (1) a green, , Total number of balls = (6 +8) = 14., Solution, , () Number of red balls = 6., , red, , Plgetting a, , )=47, , (ii) Number of green balls = 8., , 84, , Plgetting a green ball)=, AMPLE 6., , die, die is, , A, , (i), Solution, , In, , greater than 4? (iit), , throwing a die,, , all, , 7, , getting (), , probability of, , thrown. What is the, , number, , a, , 14, , a, , number not, , possible outcomes are, , greater, , a, , prime, , number?, , than 5?, , 1 2, 3, 4, 5, 6., , number of all possible outcomes = 6., , (i) Prime numbers are 2. 3, 5., Number of prime numbers = 3., , Plgetting a prime number) =, (i), , Numbers, , 4, , greater than, , are, , 31, 6, , 5 and 6., , Their number is 2., 1, , 2, , number greater than 4) =, 6, =, , a, , Plgetting, , (ii), , Nunmbers not, , greater than 5, , 3, , 1, 2, 3, 4, 5., , are, , Their number is 5., , Plgettinga, , EXAMPLE 7., , Ten cards, , number, , not greater than 5), , at, One card is chosen, and mixed thoroughly., 8?, (ii) getting, number, getting the, , (iii) getting, , of (), , a, , in, , They a r e kept, box. What, random from the, , 10 respectively., numbered as 1, 2, 3, 4, 5,.., , are, , probability, , number, , greater than 4? (iv) getting, outcomes, , Solution, , =, , Total number of possible, The number 8 is only, , one, , a, , a, , 1-digit, , number?, , in number., , (i), , 1, , Plgetting the number 8) = 10, , (ii), , Numbers, , less than 5, , are, , 1, 2, 3, 4., , 4., Their number is, , Plgettinga, (ii), , Numbers, , number less than 5), , greater than, , is, Their number, , Plgetting, , (iv) Out of given, , a, , 4, , are, , 2, =, , 10 5, , 5, 6, 7, 8, 9, 10., , 6., , number greater than 4), , numbers, the number, , of, , 9, , Plgettinga 1-digit number) =10, , =, , =°., , 1-digit numbers, , box, , is the, , 5?, number less than, , 10., , =, , a, , =, , 9.

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282, Mathematics for Class8, , EXAMPLE 8., , From a well-shuffled deck of 52 cards, one card is drawn at random. Wh, What, , PrODability that the card drawn is () a diamond?, , Solution, , Total number of all, cards 52., Total number of all, possible outcomes, (i) Number of, 13., , (i) an ace?, , is the, , (til) 5 of club?, , =, , diamonds, , =, , 13, , 1, , Plgetting a diamond) = =, 52 4, , ii) Number of all, , aces, , =, , 2, , 4., 4, , Plgetting an ace) 52, (iii) Number of 5 of club, , 13, , 1., , Plgetting 5 of club) =, 52, , EXAMPLE 9., , From a well-shufled deck of 52 cards, one card is drawn at random. Find the, , probability of getting (0) a red card. (i) a 10 of black cards, (ilt) a face card., Solutton, , Total number of all cards 52., Total number of all, possible outcomes, =, , (1) Number of red cards, , 26., , Plgetting a red card) 26, 52, , ., , 52., , =, , 1, , 2, , (ii) Number of 10s of black cards = 2., , Plgetting, , a, , 10, , 2, , of black cards), , =, , EO, 52, , 26, , (ii) Number of face cards = 12., , Plgettingaface card), , 12 3, , 52, , 13, , EXERCISE 25A, 1., , (i) A coin, , is tossed. What are all, , possible outcomes?, (ii) Two coins are tossed simultaneously. What are all possible outcomes?, (ii) A die is thrown. What are all possible outcomes?, (iv) From a well-shuffled deck of 52 cards, one card is drawn at random., What is the, number of all possible outcomes?, , 2. In a single throw of a coin, what is the probability of getting a tail?, 3. In, , a, , single, , throw of two coins, find the, , (iil) at the most 1 tail, , probability of getting (i) both tails, (ii), , at least 1 tail,, , 4. A, , bag contains 4 white and 5 blue balls. They are mixed thoroughly and one ball is drawn at, random. What is the probability of getting (i) a white ball? (ii) a blue ball?, , 5. A, , bag contains 5 white., , 6 red and 4, , green balls. One ball, , is drawn at random. What is the, , probability that the ball drawn is (i) green? (i) white? (i) non-red?, 6., , In, , a, , lottery,, , there, , are, , 10, , prizes and 20 blanks., , probability of getting a prize?, 7., , A ticket is chosen at random. What is the, , It is known that a box of 100 electric bulbs contains 8, defective bulbs. One bulb is taken, out at random from the box. What is the, probability that the bulb drawn is (i) defective?, , (ii) non-defective?

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283, , Probability, , 3, , e, , than, 2, (i) a number less, Find the probability of getting (i), random., at, not less than 4., number, (iv) a number, From, while 118 dislike it., that 82 like coffee, found, w, a, s, it, 200 ladies,, that the chosen lady, , is thrown, , 8. A d i e, ü, , ), , a, , c, , o, , m, , p, , o, , s, , i, , t, , e, , r v e v of, ladies, one is, , What is the probability, chosen at random., , In, , 9., , t h e s e, , dislikes coffee?, , numbers, , Contains, , OX, 10. A box, , from, , random, , 11., , an even, , (ii), , number,, , 19 balls bearing, that the, the probability, box. F i n d, , the, , number,, , well-shufiled, , from a, , at r a n d o m, is drawn, card, One, a king., d r a w n is (i), the card, , that, , card is, , One, , 12,, , divisible, , number, , a, , (iii), , drawn, , at, , drawn, , card, that the, , random, , (i), , is, , (ii), , a, , spade, (iii), , well-shuffled, , from a, a, , 4, (ii), , a, , a, , (iii), , queen,, , a, , is drawn at, 19 respectively. A ball, a prime, n u m b e r o n the ball is (i), , .., , 1, 2, 3,, , by 3., , cards. Find the, deck of 52, a black 8., , red, , queen,, , deck, , of 52, , probability, , (iv), , cards., , Find the, , probability, , black card., , EXERCISE 25B, , OBJECTIVE, , QUESTIONS, , answer, , Tick, , probability, , there, , wheel,, , spinning, , a, , In, , 1., , each, , of the, , sectors., , correct, , the, , (), , in, , following:, , are, , 3, , sector?, , (a) 3, , green, , a, , of getting, , 8, , (c), (b), , 8, , (a), , numbered, , 8 cards, , 2., , respectively., , 3, as, , 8, 5, 6. 7,, 1, 2, 3, 4,, the, What is, , are, , is, One c a r d, , chosen, , at, , They, , (b), What, , is the, , (b), , 4., , A, , bag, , t h a t the, , ball, , white, , drawn, , of getting, , is, A die, , 6., , is, A die, , 1, , (a)2, , drawn, , at, , (b6, thrown., , What is, , (b), , random., , What, , probability, , of getting, , one, , tail?, , probability, , 6?, , (d), , none, , number?, , the, , is the, , 5, , (c), , 1, , head and, , 1, , thrown., , 1, , one, , (d) 2, , (c), , is the, , 5, , 4, , is, One ball, , is red?, , What, , (a), , balls., , (b)3, , (a), 5., , and 2 r e d, , less, , a, , (d), (c), , 3, , mixed, , probability, , s i m u l t a n e o u s l y ., , coins are, , contains, , box a n d, , of getting, , (c), , (a), , a, , number, , probability, , tossed, , 3., , kept in, , (d), , than 4?, , Two, , are, , random., , thoroughly., , (a) 1, , the, What is, , 5 green, , and, , white, , It is spinned., , of getting, probability, , 5, , an, , even, , (d), , (c)6, , aan, , 6, , of, , these