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JEE (Main+Advanced), , Probability, , Exercise – I, Section (A) : Classical definition of probability, 1., , 2., , Two dies are rolled simultaneously. The, probability that the sum of the two numbers on, the top faces will be atleast 10 is :, (a) 1/6, (b) 1/12, (c) 1/18, (d) None, A number is chosen at random among the set of, first 120 natural numbers the probability of the, number chosen from the set being a multiple of, 5 or 15, is, , 1, 5, 1, (c), 24, (a), , 3., , 4., , 5., , 7., , 11, (a), 30, 13, (c), 30, , 47, (b), 60, , 6!6!, (a), 13!, 7!6!, (c), 14!, , 6!7!, (b), 12!, 7!6!, (d), 13!, , 8., , 9., , (d) None, , 1, 3, 1, (d), 2, , 4.13 C9 .39 C4, 52, C13, , (b), , 15 coupons are numbered 1,2,3,…,15, respectively. 7 coupons are selected at random, one at a time with replacement. The probability, that the largest number appearing on a selected, coupon is 9 is:, , 3, 5, , (c)  , , 6, , 7, , 8, (b)  ,  15 , (d), , 7, , 97  87, 157, , 2n bodys are randomly divided into two, subgroups containing n body each. The, probability that the two tallest body are in, different groups is, , n, 2n  1, 2n  1, (c), 4n 2, , (b), , n 1, 2n  1, , (d) None of these, , If M & N are any two events, then which one of, the following does not represents the probability, of the occurance of exactly one of them ?, (a) P( M )  P( N )  2 P ( M  N ), (c) P ( M )  P ( N )  2 P ( M  N ), , 10., , , , 11., , , , Thirteen persons take their places at a round, table, then the probability that two particular, persons sitting together are -, , 1, 6, 1, (c), 2, , 1, 3, 3, (d), 7, , (b), , If 12 tickets numbered 0,1,2,….11 are placed in, a bag, and three are drawn out, then the chance, that the sum of the numbers on them is equal to, 12 is -, , 2, 3, 3, (c), 59, (a), , 4!.13 C9 .39 C4, 52, C13, ,  , , (d) P M  N  P M  N, , (a), , The chance that a 13 card combination from a, pack of 52 playing cards is dealt to a specified, player in a game of bridge, in which 9 cards are, of the same suit, is, (a), , (d) None of these, , (b) P( M )  P( N )  P( M  N ), , A couple has three children. The probability of, having 2 sons and a daughter, if the eldest child, is a son, is, (b), , C9 .39 C4, 52, C13, , (a), , 7 men and 7 women can be seated at a round, table find the probability such that no two, women can sit together is, , 2, 3, 3, (c), 4, , 13, , 9, (a)  ,  16 , , In a horse race the odds in favour of three horses, are 1:2, 1:3 and 1:4. The probability that one of, the horse will win the race, , (a), , 6., , 1, 8, 1, (d), 6, , (b), , (c), , 1, 5, 3, (d), 55, (b), , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 1

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JEE (Main+Advanced), 12., , 13., , 14., , 15., , Probability, , In drawing of a card from a well shuffled, ordinary deck of playing cards the events ‘card, drawn is spade’ and ‘card drawn is an ace’ are, (a) mutually exclusive, (b) equally likely, (c) forming an exhaustive system, (d) None of these, If A and B are any event of an experiment, then, , Ac  B , (a) ( A  B)c, , 18., , 19., , (b) Ac  ( A  B), , (c) ( A  B)c, (d) A  B, A die is thrown. Let A be the event ‘an odd, number turns up’ and B be the event ‘a number, divisible by 3 turns up’. Write which of the, following are true., (i) B  A, (ii) B  A  A, c, (iii) B  A  A (iv) A  B  A  B c, (a) (i) and (ii), (b) (i), (iii), (c) (ii) and (iii), (d) (iii) and (iv), An experiment results in four possible out comes, S1 , S 2 , S3 & S 4 with, probabilities, , p1 , p2 , p3 & p4 respectively. Which one of the, , 20., , (b) p1  0.40, p2  0.20, p3  0.60, p4  0.20, , (c) p1  0.30, p2  0.60, p3  0.10, p4  0.10, 16., , (d) p1  0.20, p2  0.30, p3  0.40, p4  0.10, , There are two children in a family. The, probability that both of them are boys is, , 1, 2, 1, (c), 4, (a), , 17., , If, , A, , (b), , and, , B, , 1, 3, , (d) None of these, are, , events, , such, , that, , 3, 1, 2, P( A  B)  , P( A  B)  , P( A)  , then, 4, 4, 3, P ( A  B ) is, 5, 3, (a), (b), 12, 8, 5, 8, (c), (d), 8, 15, , (1  3 p) (1  p) (1  2 p ), ,, &, are, 3, 4, 2, , If, , 1 1 , , (a)  , , 2 3, , (b)  , , 3 2, , 4, 3, 1, (c), 3, , 3, 4, 3, (d), 5, , 2, 3, , 1, 2, 1, (d), 3, , 1 1, , 21., , the, , probabilities of three pair wise exclusive events, then the set of all values of p is ., , 1 2, , following probability assignment is possible., [Assume S1S2 S3 S4 are pair wise exclusive], , (a) p1  0.25, p2  0.35, p3  0.10, p4  0.05, , Out of 13 applicants for a job, there are 5, women and 8 men. It is desired to select 2, persons for the job. The probability that at least, one of the selected persons will be a woman is, (a) 25/39, (b) 14/39, (c) 5/13, (d) 10/13, There are three events A, B, C, one of which, must, and only one can, happen; the odds are 8, to 3 against A, 5 to 2 against B. The odds against, C are, (a) 34 : 43, (b) 43 : 34, (c) 53 : 45, (d) 43 : 53, , 1 2 , , (c)  , , (d)  , , 4 2, 3 3, If 3 events A, B, C are exhaustive, then value of, P( A)  P( B)  P(C ) can be, (a), , (b), , Section (C) : Conditional probability, dependent and, independent events, 22., In throwing a pair of dice, the events ‘coming up, of 6 on lst die’ and ‘a total of 7 on both the dies’, are, (a) mutually exclusive, (b) forming an exhaustive system, (c) independent, (d) dependent, 23., A fair die is tossed. If the number is odd, find, the probability that it is prime is, (a), , 24., , Section (B) : Addition theorem, , (c) 1, , (b), , A card is drawn from a well shuffled ordinary, deck of 52-playing cards. The card drawn is, found to be a spade. Then the probability that, the card is an ace, is, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 2

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JEE (Main+Advanced), , 1, 13, 1, (c), 4, (a), , 25., , Probability, , 1, 52, 1, (d), 8, , (b), , A pair of dice is thrown. If total of numbers, turned up on both the dies is 8, then the, probability that the number turned up on the, second die is 5’ is, , 5, (a), 36, 1, (c), 5, , 26., , 1, (b), 6, 2, (d), 5, , A bag contains 2 white & 4 black balls. A ball is, drawn 5 times, each being replaced before, another is drawn. The probability that atleast 4, of the balls drawn are white is :, (a) 4/81, (b) 10/243, (c) 11/243, (d) 8/243, A & B having equal skill, are playing a game of, best of 5 points. After A has won two points &, B has won one point, the probability that A will, win the game is :, (a) 1/2, (b) 2/3, (c) 3/4, (d) 1/4, If odds against solving a question independently, by three students are 2 :1, 5 : 2 and 5 : 3, respectively, then probability that the question is, solved only by one student is, , 27., , 28., , 31, 56, 25, (c), 56, (a), , 29., , 24, 56, 29, (d), 56, (b), , A die is weighted so that the probability of, different faces to turn up is as given, , If, , Number, Probability, , 1, 2, 3, 4, 5, 6, 0.2 0.1 0.1 0.3 0.1 0.2, P( A / B)  p1 and, P ( B / C )  p2 and, , P(C / A)  p3 then the values of p1 , p2 , p3, , respectively are – Take the events A, B & C as, A  {1, 2,3}, B  {2,3,5} and C  {2, 4, 6}, , 2 1 1, , ,, 3 3 4, 1 1 1, (c) , ,, 4 3 6, (a), , 1 1 1, , ,, 3 3 6, 2 1 1, (d) , ,, 3 6 4, (b), , 30., , If A and B are independent events and, , 31., , (a) 1, (c) 3, If, , 32., , 1, 2, P( A  B)  , P( A)  , then 6 P( B / A) , 6, 3, (b) 2, (d) 4, , P( A)  0.4, P( B)  0.48 and, P( A  B)  0.16, then the value of P( A / B ) is, , (a) 1/3, (b) 2/3, (c) 1/4, (d) 1/6, Let 0  P( A)  1,0  P(B)  1& P( A  B)  P( A)  P(B)  P( A),, then:, (a) P( B / A)  P( B)  P( A), (b) P( Ac  B c )  P( Ac )  P( B c ), (c) P (( A  B )c )  P( Ac ).P( B c ), , 33., , (d) P( A / B)  P( A)  P( B), If M & N are independent events such tat, 0  P(M )  1& 0  P( N )  1, then choose the, incorrect option, (a) M & N are mutually exclusive, (b) M & N are independent, (c) M & N are independent, , (d) P ( M / N )  P ( M / N )  1, Section (D) : Total probability theorem, Baye’s, theorem, 34., 2/3rd of the students in a class are boys & the rest, girls. It is known that probability of a girl getting, a first class is 0.25 & that of a boy is 0.28. The, probability that a student chosen at random will, get a first class is :, (a) 0.26, (b) 0.265, (c) 0.27, (d) 0.275, 35., In a Aeroplane there are 2 pilots and 3 doctors, and in another Aeroplane there are 4 points and, 2 doctors one Aeroplane is selected at random, and a person is selected. Then the probability the, chosen person is pilot is, , 2, 15, 8, (c), 15, (a), , 36., , 7, 15, 14, (d), 15, (b), , A basket contains 5 apples and 7 oranges and, another basket contains 4 apples and 8 oranges., One fruits is picked out form each basket. Find, the probability that both fruits are apples or both, are oranges, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 3

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JEE (Main+Advanced), , 24, 144, 68, (c), 144, (a), , 37., , Consider, , 56, 144, 76, (d), 144, , Probability, , (b), , two, , sets, , 41., , P  {a, b, c, d , e} and, , Q  { f , g , h, i, j} A person selects a set P with, 1, 2, probability or set Q with probability, and, 3, 3, , forms a subset R of two elements both selected, from set P or Q. Find probability that set R, consists of one vowel & one consonants, , 1, 5, 2, (c), 15, (a), , 38., , 3, 11, 7, (d), 15, , i2  1, urn is, (i  1, 2,3, 4). If we randomly, 34, , select one of the urns & draw a ball, then the, probability of ball being white is :, , 569, 1496, 8, (c), 73, (a), , 39., , Two cards are drawn successively from a wellshuffled ordinary deck of 52-playing cards, without replacement and is noted that the second, card is a king. The probability of the event ‘first, card is also a ‘king’ is, , 2, 19, 3, (c), 49, , 1, 17, 4, (d), 5, A bag contains (n  1) coins. It is known that, (a), , 40., , 27, 56, 729, (d), 1496, (b), , (b), , one of these coins has a head on both sides,, whereas the other coins are normal. One of these, coins is selected at random & tossed. If the, probability that the toss results in head, is 7/12,, then the value of n is., (a) 5, (b) 6, , 125, 287, 25, (c), 287, (a), , (b), , There are 4 urns. The first urn contains 1 white, & 1 black ball, the second urn contains 2 white, & 3 black balls, the third urn contains 3 white &, 5 black balls & the fourth urn contains 4 white, & 7 black balls. The selection of each urn is not, equally likely. The probability of selecting ith, , (c) 4, (d) 3, The contents of urn I and II are as follows,, Urn I: 4 white and 5 black balls, Urn II : 3 white and 6 black balls, One urn is chosen at random and a ball is drawn, and its colour is noted and replaced back to the, urn. Again a ball is drawn from the same urn,, colour is noted and replaced. The process is, repeated 4 times and as a result one ball of white, colour and 3 of black colour are noted. Find the, probability the chosen urn was I., , 42., , 64, 127, 79, (d), 192, (b), , A box contains 4 white and 3 black balls. Two, balls are drawn successively and is found that, second ball is white, then the probability that Ist, ball is also white is, , 5, 16, 1, (c), 5, (a), , 1, 2, 1, (d), 3, , (b), , Section (E) : Probability distribution and binomial, probability distribution, 43., Mean and variance of a Binomial variate are in, the ratio of 3 : 2. The most probable number of, happening of the variable in 10 trials of the, experiment is, (a) 2, (b) 3, (c) 4, (d) 5, 44., A die is tossed thrice. A success is getting 1 or 6, on a toss. The mean and the variance of number, of successes, (a)   1,  2  2 / 3 (b)   2 / 3,  2  1, , 45., , 46., , (c)   2,  2  2 / 3 (d) None of these, In a series of 3 independent trials the probability, of exactly 2 success is 12 times as large as the, probability of 3 successes. The probability of a, success in each trial is :, (a) 1/5, (b) 2/5, (c) 3/5, (d) 4/5, If one an average 1 vessel in every 10 is, wrecked, then the chance that out of 5 vessels, expected 4 at least will arrive safely is, (a), , 45981, 50000, , (b), , 1, 10, , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 4

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JEE (Main+Advanced), , 47., , 48., , 49., , 50., , (c), , 45927, 50000, , Probability, , (d) 1, , A fair coin is tossed 99 times. If X is the number, of times heads occur, then P ( X  r ) is, maximum when r is, (a) 49, (b) 50, (c) 51, (d) 49 or 50, An unbiased coin is tossed n times. Let X denote, the number of times head occurs. If, P( X  4), P( X  5) and P( x  6) are in AP,, then the value of n can be, (a) 9, (b) 10, (c) 12, (d) 14, India decides to destroy one of the militants, holdings. In the bombing attack there is 50%, chance of a bomb hitting the target, only two, direct bomb hits are required to destroy the, target completely. Least number of bombes, required to give 99% chance or better of, completely destroying the target is, (a) 9, (b) 10, (c) 11, (d) 12, A pair of dice is thrown 5 times, then the, probability of getting a doublet exactly two, times is -, , 25, 377, 625, (c), 1944, (a), , Answer Key, 1, a, 11, d, 21, a, 31, a, 41, a, , 2, a, 12, d, 22, c, 32, c, 42, b, , 3, c, 13, c, 23, a, 33, a, 43, b, , 4, d, 14, d, 24, a, 34, c, 44, a, , 5, d, 15, d, 25, c, 35, c, 45, a, , 6, a, 16, c, 26, c, 36, d, 46, c, , 7, d, 17, a, 27, c, 37, d, 47, d, , 8, a, 18, a, 28, c, 38, a, 48, d, , 9, b, 19, b, 29, d, 39, b, 49, c, , 10, a, 20, b, 30, c, 40, a, 50, b, , 625, 3888, 25, (d), 972, , (b), , ADDRESS : NEAR CANARA BANK, JAIL BYPASS ROAD, PADRI BAZAR, GORAKHPUR,, MOB: 6386566032,7992166350, , 5