MathsMaths QuestionsProbability Ii Questions for CBSE Class 12th

Probability Ii Questions for CBSE Class 12th

If the integer s m and n are chosen at random between 1 and 100, then the probability that a number of the form 7 m + 7 n is divisible by 5 equals

A cricket club has 15 members, of whom only 5 can bowl. If the names of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven containing at least 3 bowlers is

    Fill Out the Form for Expert Academic Guidance!



    +91


    Live ClassesBooksTest SeriesSelf Learning




    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is

    If the letters of the word ‘REGULATIONS’ are arranged at random, then the probability that there will be exactly 4 letters between R and E is

    A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3, and 1/4. Probability that the problem is solved is

    Let A and B be two independent events such that P ( A ) = 1 3 and P ( B ) = 1 6 . Then, which of the following is TRUE?

    An ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is:

    A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, then the probability that the other is also good, is

    One hundred identical coins, each with probability p , of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then value of p is

    The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of at least 2 successes is

    The probability that in a family of five members, exactly two members have birthday on Sunday is

    If A and B are two possible events which satisfy P ( A ∪ B ) = P ( A ∩ B ) , then which of the following is always true?

    In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 1 4 . If the probability that at most two machines will be out of service on the same day is 3 4 3 k then k is equal to:

    In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is:

    A signal which can be green or red with probability 4 5 and 1 5 respectively is received by the station A and Transmitted to B . The probability of each station receiving signal correctly is 3 4 . If signal in received in B is green. The probability original signal was green is

    If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

    A draws a card from a pack of n cards marked 1,2,……n. The card is replaced in the pack and B draws a card. Then the probability that A draws a higher card than B is

    Let A and B are any two events such that P ( A ) = 1 2 and P ( B ) = 1 3 then the value of P A c ∩ B c c + P A c ∪ B c c has the value =

    Twelve balls are distributed among three boxes. The probability that the first box contains three balls is

    Two numbers a? b are chosen from the set of integers 1, 2, 3, .…. 39.Then probability that the equation 7a – 9b = 0 is satisfied is

    One mapping is selected at random from all mappings of the set s – {1, 2, 3, . . . n} into itself. If the probability that the mapping is one-one is 3/32, then the value of n is

    Two persons each makes a single throw with a pair of dice. The probability that their scores are equal is

    Two dices are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

    A box contains tickets numbered from I to 20. Three tickets are drawn from the box with replacement. The probability that the largest number on the tickets is 7 is

    Three ships A, B, and C sail from England to India. If the ratio of their arriving safely are 2;5, 3:7 , and 6: 11, respectively, then the probability of all the ships for arriving safely is

    Let 0 < P ( A ) < 1 , 0 < P ( B ) < 1 and P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ) P ( B ) , then

    Let A and B be two events. Suppose P ( A ) = 0.4 , P ( B ) = p , and P ( A ∪ B ) = 0.7 . The value of p for which A and B are independent is

    Let A, B, C be three mutually independent events. Consider the two statements S 1 and S 2 . S 1 : A and B ∪ C are independent S 2 : A and B ∩ C are independent Then,

    The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die is

    All the jacks, queens, kings, and aces of a regular 52 cards deck are taken out. The 16 cards are thoroughly shuffled and my opponent, a person who always tells the truth, simultaneously draws two cards at random and says, “I hold at least one ace”. The probability that he holds two aces is

    Let A and B arc events of an experiment and P ( A ) = 1 / 4 , P ( A ∪ B ) = 1 / 2 , then value of P B / A c is

    An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, other wise X takes the value -1.The expected value of X, is:

    Four persons can hit a target correctly with probabilities 1 2 , 3 4 , 1 4 and 1 8 respectively. If all hit at the target independently, then the probability that the target would be hit, is

    A and B are two candidates seeking admission in IIT. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3.The probability of B getting selected cannot exceed.

    Three integers are chosen from 1 to 20 without replacement. Probability that their product is even, is

    L e t A d e n o t e t h e e v e n t t h a t a 6 – d i g i t i n t e g e r f o r m e d b y 0 , 1 , 2 , 3 , 4 , 5 , 6 w i t h o u t r e p e t i t i o n s , b e d i v i s i b l e b y 3 . T h e n p r o b a b i l i t y o f e v e n t A i s e q u a l t o :

    A biased coin with probability P , 0 < P < 1 of head, is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2 5 , then the value of P is

    Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the top faces of two cubes shows the same colouris 1 2 . Then number of red faces on the second cube is

    A coin whose faces are marked 3 and 5 is tossed 4 times. The probability that the sum of the numbers thrown is greater than 15 is

    A positive integer n not exceeding 100 is chosen at random in such a way that, p is the probability of choosing n ≤ 50 and 3 p is the probability of choosing n > 50 . If λ is probability that a perfect square is chosen, then the value of [ 100 λ ] ([.] GIF)

    A bag contains 2 n + 1 coins. It is known that n of these coins have a head on both sides where as the rest of the coins are fair. A coin is picked up at random form the bag and is tossed. If the probability that the results in a head is 31 42 , then the value of n is

    Fifteen coupons ate numbered 1, z, 3, 15. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on selected coupon is 9 is

    For the three events A , B and C , P ( exactly one of the events A or B occurs ) = P ( exactly one of the two events B or C occurs ) = P ( exactly one of the events C or A occurs ) = p and P ( all the three events occur simultaneously ) = p 2 where 0 < p < 1 / 2 . Then the probability of at least one of the three events A , B and C occurring is

    Let ω be a complex cube root of unity with ω ≠ 1 . A fair die is thrown three times. If r 1 , r 2 and r 3 are the numbers obtained on the die, then the probability that ω r 1 + ω r 2 + ω r 3 = 0 is

    A natural number is chosen at random from the first 100 natural numbers. The probability that x + 100 x > 50 is

    If a is an integer lying in [ − 5 , 30 ] , then the probability that the graph of y = x 2 + 2 ( a + 4 ) x − 5 a + 64 is strictly above the x -axis is

    Consider f ( x ) = x 3 + a x 2 + b x + c . Parameters a , b , c are chosen, respectively, by throwing a die three times. Then the probability that f ( x ) is an increasing function is

    In a game called ‘odd man out’ , m (m > 2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is

    Let A , B , C be three events. If the probability of occurring exactly one event out of A and B is 1 − a , out of B and C is 1 − 2 a , out of C and A is 1 − a and that of occurring three events simultaneously is a 2 , then the probabil ity that at least one out of A , B , C will occur is

    Let the 9 different letters A , B , C , … , I ∈ { 1 , 2 , 3 , … 9 } then the probability that product ( A − 1 ) ( B − 1 ) … ( I − 9 ) is even number will be

    Consider a set P containing n elements. A subset A of P is drawn and there after set P is reconstructed. Now one more subset B of P is drawn. Probability of drawing sets A and B so that A ∩ B has exactly one element is

    India plays two matches each with West Indies and Australia. In any match, the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.50, respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is

    A six-faced fair dice is shown until 1 comes. Then the probability that 1 comes in even number of trials is

    A box contains 24 identical balls of which 12 are white and 12 are black. The balls are drawn at random from the box one at a time with replacement. The probability that a white ball is drawn for the 4th time on the 7th draw is

    A coin is flipped seven times. If the probability that it comes up head at least 4 times in a row is

    A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is

    Cards are drawn one-by-one at random from a well-shuffled pack of 52 playing cards until 2 aces are obtained from the first time. The probability that 18 draws are required for this is

    A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

    A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

    If p is the probability that a man aged x will die in a year, then the probability that out of n men A 1 , A 2 , … , A n each aged x , A 1 will die in an year and be the first to die is

    A bag contains a white and b black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, the ratio a:b is

    A speaks truth in 60% cases and B speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is

    If A and B are two independent events such that P ( A ∩ B ) = 2 / 15 and P ( A ∩ B ) = 1 / 6 , then P ( B ) is

    If A and B are two events such that P ( A ) > 0 and P ( B ) ≠ 1 then P ( A / B ) is equal to (Here, A ¯ and B ¯ are complements of A and B , respectively)

    One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

    Let E C denote the complement of an event E . Let E , F , G be pairwise independent events with P ( G ) > 0 and P ( E ∩ F ∩ G ) = 0 . Then P E C ∩ F C / G equals

    Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is

    A signal which can be green or red with probability 2 3 and 1 5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3 4 If the signal received at station B is green, then the probability that the original signal was green is

    A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighborhood are sick with the flu, denoted by F, while 10% are sick with the measles, denoted by M. A well known symptom of measles is a rash, denoted by R. The probability of having a rash for a child sick with the measles is 0.95. However, occasionally children with the flu also develop a rash, with conditional probability 0.08. Upon examination the child, the doctor finds a rash. Then what is the probability that the child has the measles?

    A bag has 10 balls. Six balls are drawn in an attempt and replaced. Then another draw of 5 balls is made from the bag. The probability that exactly two balls are common to both the draw is

    Given four pair of gloves, they are distributed to four persons. Each person is given a right handed and left handed glove, the probability that no person gets a pair is equal to

    A bag contains 10 balls of which 2 are red and the remaining are either blue or black. If the probability drawing 3 balls of the same colour is 11 20 and if the number of blue balls exceeds the number of black balls, the number of blue balls is

    The probability of a man hitting a target in one fire is 1 5 . Then the minimum number of fire he must follow in order to make his chance of hitting the target more than 3 4 is

    A and B are 2 events such that P ( A ) = 3 4 and P ( B ) = 5 8 . If a and b are the possible minimum and maximum values of P ( A ∩ B ) , then the value of a + b is

    If the probability that the product of the outcomes of three rolls of a fair dice is a prime number p then the value of 3p is

    A person is known to speak truth 3 out of 4 times. He throws a dice and responds that it is a six. Then the probability that it is actually a six is

    Suppose A and B are two events with P ( A ) = 0.5 and P ( A ∪ B ) = 0.8 . Let P ( B ) = p if A and B are mutually exclusive and P ( B ) = q if A and B are independent events then the value of q / p is

    Two different numbers are taken from the set {0, I ,2,3,4,5,6,7,8, 9, 10).The probability that their sum and positive difference, are both multiple of 4, is x 55 then x equals

    There are two red, two blue, two white and certain number (greater than 0) of green socks Ln a drawer. If two socks are taken at random from the drawer without replacement, the probability that they are of the same colour is 1/5 then the number of green socks is-‘

    If two loaded dice each have the property that 2 or 4 is three times as likely to appear as 1, 3, 5 or 6 on each roll. When two such dice are rolled, the probability of obtaining a total of 7 is p then the value of 1 / p is (where [.] represents the greatest integer function)

    Two events A and B have probabilities 0.25 and 0.50,respectively. The probability that both A and B occur simultaneously is 0.14. Then the probability that neither A nor B occurs is

    Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is

    If P B = 3 4 , P A ∩ B ∩ C ¯ = 1 3 and P A ¯ ∩ B ∩ C ¯ = 1 3 , then P B ∩ C is

    If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is

    Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both B’s are not together and both . I ‘s are not together is

    A four figure number is formed of the figures 1,2,3,5 with no repetitions. The probability that the number is divisible by 5 is

    Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is

    If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

    Let E be an event which is neither a certainty nor an impos- sibility. If probability is such that P ( E ) = 1 + λ + λ 2 and P E ′ = ( 1 + λ ) 2 in terms of an unknown λ . Then P ( E ) is =

    A bag contains 50 tickets numbered 1, 2, 3, . . ., 50 of which five are drawn at random and arranged in ascending order of magnitude x 1 < x 2 < x 3 < x 4 < x 5 . . The probability that x 3 = 30 is

    A card is drawn from a pack of 52 cards. A gambler bets that it is a spade or an ace. What are the odds against his winning this bet?

    The chance that the vowels are separated in an arrangement of the letters of the word “HORROR” is

    If the letters of the word MATHEMATICS are arranged arbitrarily, the probability that C comes before E, E before H,H before I and I before S is

    A draws a card from a pack of n cards marked 1,2,……..n. The card is replaced in the pack and B draws a card. Then the probability that A draws a higher card than B is

    Two numbers are selected randomly from the set S = {1,2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4is

    Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

    A class consists of 80 students, 25 of them are girls and 55 are boys. If 10 of them are rich and the remaining are poor and also 20 of them are intelligent, then the probability of selecting an intelligent rich girl is

    A person throws a dice while he gets a number greater than 2. The probability that he gets a 6 in the last throw is

    Let A and B be two events such that P ( A ∪ B ¯ ) = 1 / 6 , P ( A ∩ B ) = 1 / 4 and P ( A ¯ ) = 1 / 4 , where A ¯ stands for complement of event A . Then events A and B are

    Events A and C are independent. If the probabilities relating A , B , and C are P ( A ) = 1 / 5 , P ( B ) = 1 / 6 ; P ( A ∩ C ) = 1 20 P ( B ∪ C ) = 3 / 8 . Then

    The probability of India winning a test match against West Indies is 1 2 . Assuming independence from match to match, the probability that in a five match series India’s second win occurs at third test is

    The probabilities of winning a race by three persons A, B, and C are 1 2 , 1 4 , and 1 4 , respectively. They run two races. The probability of A winning the second race when B, wins the first race is

    It is given that the events A and B are such that P ( A ) = 1 4 , P A B = 1 2 , P B A = 2 3 then P ( B ) =

    Of all the mappings that can be defined from the set A : {1,2,3, 4} B : {5, 6,7 ,8, 9} , a mapping is randomly selected. The chance that the selected mapping is strictly monotonic is

    A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is

    There are 20 cards. Ten of these cards have the letter “I” printed on them and the other 10 have the letter “T” printed on them. If three cards are picked up at random and kept in the same order, the probability of making word IIT is

    One ticket is selected at random from 100 tickets numbered 00 , 01 , 02 , … , 99 . Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then P ( ( A = 7 ) / ( B = 0 ) ) is given by

    Let A and B be two events such that P A ∩ B ′ = 0 .20 P A ′ ∩ B = 0 .15 , P A ′ ∩ B ′ = 0 .1 , then P(A/B) is equal to

    A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is

    The probability that an automobile will be stolen and found within one week is 0.0006. The probability that an automobile will be stolen is 0.0015. The probability that a stolen automobile will be found in one week is

    One ticket is selected at random from 100 tickets numbered 00 , 01 , 02 , … , 99 . Suppose A and B are the sum and product of the digit found on the ticket, respectively. Then P ( ( A = 7 ) / ( B = 0 ) ) is given by

    A pair of numbers is picked up randomly (without replacement) from the set {1, 2, 3,5, 7, 11, 12, 13, 17, 19). The probability that the number 11 was picked given that the sum of the numbers was even is nearly

    In a certain town, 40% of the people have brown hair, 25% have brown eyes, and 15% have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is

    A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even is

    A bag contains m white and n black balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consists of one white and one black ball is

    Cards are drawn one-by-on e at random from a well-shuffled pack of 52 playing cards until 2 aces are obtained from the first time. The probability that 18 draws are required for this is

    Two dices are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

    Let A, B, C be three mutually independent events. Consider the two statements S 1 and S 2 . S 1 : A and B ∪ C are independent. S 2 : A and B ∩ C are independent. Then

    One ticket is selected at random from 50 tickets numbered 00, 01, 02, …, 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals

    The probability that a student is not a swimmer is 1 / 5 . The probability that out of 5 students exactly 4 are swimmer is

    Chat on WhatsApp Call Infinity Learn

      Talk to our academic expert!



      +91


      Live ClassesBooksTest SeriesSelf Learning




      Verify OTP Code (required)

      I agree to the terms and conditions and privacy policy.