Class 11 Mathematics Probability MCQs Set D

Question. From a book containing 100 pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is 11, is:
(a) 2/25
(b) 9/100
(c) 11/100
(d) None of these      A

Answer: A

Question. One card is drawn from each of two ordinary packs of 52 cards. The probability that at least one of them is an ace of heart, is:
(a) 103/2704
(b) 1/2704
(c) 2/52/
(d)2601/2704     

Answer: A

Question. A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is:
(a) 5/11
(b) 21/55
(c) 4/11
(d) None of these   

Answer: B

Question. If Mohan has 3 tickets of a lottery containing 3 prizes and 9 blanks, then his chance of winning prize are:
(a) 34/55
(b) 21/55
(c) 17/55
(d) None of these   

Answer: A

Question. Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to:
(a) 27/1
(b) 9/1
(c) 27/4
(d) 6/1   

Answer: D

Question. From 10,000 lottery tickets numbered from 1 to 10,000,one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by 20?
(a) 1/100
(b) 1/50
(c) 1/20
(d) 1/10   

Answer: C

Question. A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is
(a) 3/2
(b) 4/3
(c) 5/4
(d) 5/3   

Answer: D

Question. A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is:
(a) 1/52
(b) 1/26
(c) 1/18
(d) None of these 

Answer: B

Question. Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11?
(a) 17/18
(b) 1/12
(c) 11/12
(d) None of these 

Answer: C

Question. Given two mutually exclusive events A and B such that P(A) = 0.45 and P(B) = 0.35, then P (A or B) = ?
(a) 0.1
(b) 0.25
(c) 0.15
(d) 0.8 

Answer: D

Question. In a class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is:
(a) 25/13
(b) 25/3
(c) 25/17
(d) 25/8   

Answer: A

Question. A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is 1/3. What is the probability that none of them will be selected?
(a) 1/2
(b) 1/12
(c) 1/4
(d) None of these     

Answer: D

Question. A ship is fitted with three engines E₁, E₂ and E₃.
The engines function independently of each other with respective probabilities 1/2, 1/4, and 1/4. For the ship to be operational atleast two of its engines must function. Let X denote the event that the ship is operational and let X₁,X₂ and X₃ denotes, respectively the events that the engines E₁,E₂ and E₃ are functioning. Which of the following is/ are true?
(a) P[X₁⁰ | X] = 3/16
(b) P[Exactly two engines of the ship are functioning x] = 7/8
(c) P[X | X₂] = 5/16
(d) P[X | X₁] = 7/16   

Answer: B,D

Question. Let X and Y be two events such that P(X/Y) =1/2 , P(Y/X) =1/3 and P (X∩Y) Which of the following is/are correct?
(a) P(X∪Y) = 2 / 3
(b) X and Y are independent
(c) X and Y are not independent
(d) P (X^c∩Y) = 1/3     

Answer: A,B

Question. The probability that an event will fail to happen is 0.05.
The probability that the event will take place on 4 consecutive occasions is:
(a) 0.00000625
(b) 0.18543125
(c) 0.00001875
(d) 0.81450625 

Answer: D

Question. Two fair dice are tosse(d) Let A be the event that the first die shows an even number and B be the event that second die shows an odd number. The two events A and B are:      
(a) Mutually exclusive
(b) Independent and mutually exclusive
(c) Dependent
(d) None of these   

Answer: D

Question. The probabilities of a student getting I, II and III division in an examination are respectively 1/10 , 3/5 and 1/4. The probability that the student fail in the examination is:
(a) 197/200
(b) 27/200
(c) 83/100
(d) None of these   

Answer: D

Question. Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, is equal to:
(a) 1/2
(b) 1/5
(c) 1/10
(d) 1/20   

Answer: C

Question. Let p denotes the probability that a managed x years will die in a year. The probability that out of n men A1,A2,A3,An each aged x, A1 will die in a year and will be the first to die, is:
(a) 1/n[1–(1–P)n]
(b) [1–(1–P)n]
(c) 1/n–1[1–(1–P)n]
(d) None of these 

Answer: A

Question. In a bolt factory, machines A, B and C manufacture respectively 25%, 35% and 40% of the total bolts. Of their output 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. Then the probability that the bolt drawn is defective is
(a) 0.0345
(b) 0.345
(c) 3.45
(d) 0.0034   

Answer: A

Question. There are four letters and four addressed envelopes. The chance that all letters are not dispatched in the right envelope is:
(a) 19/24
(b) 21/23
(c) 23/24
(d) 1/24   

Answer: C

Question. The letters of the word ‘ASSASSIN’ are written down at random in a row. The probability that no two S occur together is:
(a) 1/35
(b) 1/14
(c) 1/15
(d) None of these   

Answer: B

Question. From a pack of 52 cards two are drawn with replacement.
The probability, that the first is a diamond and the second is a king, is:
(a) 1/26
(b) 17/2704
(c) 1/52
(d) None of these 

Answer: C

Question. A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is:
(a) 1
(b) 1/3
(c) 7/36
(d) None of these   

Answer: B

Question. If the odds against an event be 2 : 3, then the probability of its occurrence is:
(a) 1/5
(b) 2/5
(c) 3/5
(d) 1     

Answer: C

Question. 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?
(a) 17 : 52
(b) 52 : 17
(c) 9 : 4
(d) 4 : 9     

Answer: C

Question. Two cards are drawn at random from a pack of 52 cards. The probability that both are the cards of spade is:
(a) 1/26
(b) 1/4
(c) 1/17
(d) None of these

Answer: C

Question. If odds against solving a question by three students are 2:1, 5 : 2 and 5 : 3 respectively, then probability that the question is solved only by one student is:
(a) 31/56
(b) 24/56
(c) 25/56
(d) None of these   

Answer: C

Question. A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is:
(a) 1/13
(b) 1/26
(c) 1/2
(d) 7/13   

Answer: D

Question. A man draws a card from a pack of 52 playing cards,replaces it and shuffles the pack. He continues this processes until he gets a card of spade. The probability that he will fail the first two times is:
(a) 9/16
(b) 1/16
(c) 9/64
(d) None of these     

Answer: C

Question. In a city 20% persons read English newspaper, 40% read Hindi newspaper and 5% read both newspapers. The percentage of non-reader either paper is
(a) 60%
(b) 35%
(c) 25%
(d) 45%   

Answer: D

Question. A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are ruste(d) If one item is chosen at random, what is the probability that it is rusted or is a nail:
(a) 3/16
(b) 5/16
(c) 11/16
(d) 14/16     

Answer: C

Question. A bag contains 3 red, 7 white and 4 black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is:
(a) 6/71
(b) 7/81
(c) 10/91
(d) None of these   

Answer: C

Question. A box contains 25 tickets numbered 1, 2,...25. If two tickets are drawn at random then the probability that the product of their numbers is even, is:
(a) 11/50
(b) 13/50
(c) 37/50
(d) None of these   

Answer: C

Question. A bag contains 4 white, 5 red and 6 black balls. If two balls are drawn at random, then the probability that one of them is white is:
(a) 44/105
(b) 11/105
(c) 11/ 21
(d) None of these   

Answer: A

Question. If the probability of a horse A winning a race is 1/4 and the probability of a horse B winning the same race is 1/5, then the probability that either of them will win the race is:
(a)1/20
(b) 9/20
(c) 11/20
(d) 19/20       

Answer: B

Question. The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is:
(a) p + q
(b) p + q − 2qp
(c) p + q − pq
(d) p + q + pq     

Answer: B

Question. A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is:
(a) 1/2
(b) 5/9
(c) 4/9
(d) 2/9     

Answer: C

Question. In a lottery 50 tickets are sold in which 14 are of prize. A man bought 2 tickets, then the probability that the man win the prize, is:
(a) 17/35
(b) 18/35
(c) 72/175
(d) 13/175   

Answer: A

Question. The probability of getting a total of 5 or 6 in a single throw of 2 dice is:
(a) 2/1
(b) 4/1
(c) 3/1
(d) 6/1   

Answer: B

Question. The probability of happening an event A in one trial is 0.4. The probability that the event A happens at least once in three independent trials is:
(a) 0.936
(b) 0.784
(c) 0.904
(d) 0.216   

Answer: B

Question. A three digit number is formed by using numbers 1, 2, 3 and 4. The probability that the number is divisible by 3, is:
(a) 2/3
(b) 2/7
(c) 1/2
(d) 3/4     

Answer: C

Question. Three identical dice are rolle(d) The probability that same number will appear on each of them will be:
(a) 1/6
(b) 1/36
(c) 1/18
(d) 3/28   

Answer: B

Question. A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is:
(a) 2/11
(b) 3/11
(c) 4/11
(d) 0   

Answer: C

Question. Word ‘UNIVERSITY’ is arranged randomly. Then the probability that both ‘I’ does not come together, is:
(a) 3/5
(b) 2/5
(c) 4/5
(d) 1/5   

Answer: C

Question. A bag has 13 red, 14 green and 15 black balls. The probability of getting exactly 2 blacks on pulling out 4 balls is P1. Now the number of each colour ball is doubled and 8 balls are pulled out. The probability of getting exactly 4 blacks is P2. Then:
(a) P1 = P2
(b) P1 > P2
(c) P1 < P2
(d) None of these   

Answer: B

Question. Two friends A and B have equal number of daughters.There are three cinema  tickets which are to be distributed among the daughters of A and (b) The probability that all the tickets go to daughters of A is 1/20. The number of daughters each of them have is:
(a) 4
(b) 5
(c) 6
(d) 3   

Answer: D

Question. Two dice are tossed together. The odds in favour of the sum of the numbers on them as 2 are:
(a) 1:36
(b) 1:35
(c) 35:1
(d) None of these   

Answer: B

Question. The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the students has a 75% chance of passing in at least one, a 50% chance of passing in at least two, and a 40% chance of passing in exactly two. Which of the following relations are true?
(a) p + m+ c = 19/20
(b) p + m+ c = 27/20
(c) pmc = 1/10
(d) pmc = 1/4     

Answer: B,C

Question. Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then:
(a) P(E) = 4/5 , P(F) = 3/5
(b) P(E) = 1/5 , P(F) = 2/5
(c) P(E) = 2/5 , P(F) = 1/5
(d) P(E) = 3/5 , P(F) = 4/5   

Answer: A,D