# MCQs for Mathematics Class 11 with Answers Chapter 16 Probability

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Probability with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

**Chapter 16 Probability MCQ with Answers Class 11 Mathematics**

MCQ Questions Class 11 Mathematics Probability with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee?**

(a) (^{38}C_{3})

(b) (^{37}C_{2})

(c) (^{37}C_{2}) /(^{38}C_{3})

(d) 666/8436

## Answer

C

**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: A five digit number is chosen at random. The probability that all the digit are distinct and digits at odd places are odd and digits at even place are even, is**

(a) 1/60

(b) 2/75

(c) 1/50

(d) 1/75

## Answer

D

**Question: If from each of three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be****drawn, is**

(a) 13/32

(b) 1/4

(c) 1/32

(d) 3/16

## Answer

A

**Question: A three digit number, which is a multiple of 11, is chosen at random. Probability that the number so chosen is also a multiple of 9, is equal to**

(a) 1/9

(b) 2/9

(c) 1/100

(d) 9/100

## Answer

D

**Question: There are four machines and it is known that exactly two of them are faulty. They are tested, one-by-one in a random order till both the faulty machines are identified. Then, the probability that only two tests** **are needed, is**

(a) 1/3

(b) 1/6

(c) 1/2

(d) 1/4

## Answer

B

**Question: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**

(a) 18/595

(b) 6/17

(c) 3/10

(d) 2/7

## Answer

A

**Question: There are 9999 tickets bearing numbers 0001, 0002, … , 9999. If one ticket is selected from these tickets at random, the probability that the number on the ticket will consists of all different digits, is**

(a) 5040/9999

(b) 5000/9999

(c) 5030/9999

(d) None of these

## Answer

A

**Question: Thirty two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is**

(a) 16/31

(b) 1/2

(c) 17/31

(d) None of these

## Answer

A

**Question: 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**

(a) 1/3

(b) 1/2

(c) 1/4

(d) 2/3

## Answer

B

**Question: The probability of solving a question by three students are 1/2, 1/4, 1/6, respectively. Probability of question being solved will be**

(a) 33/48

(b) 35/48

(c) 31/48

(d) 37/48

## Answer

A

**Question: A bag contains 5 white and 3 black balls and 4 balls are successively drawn out and not replaced. The probability that they are alternately of different colours, is**

(a) 1/196

(b) 2/7

(c) 13/56

(d) 1/7

## Answer

D

**Question: Three numbers are chosen from 1 to 20. Find the probability that they are not consecutive.**

(a) 186/190

(b) 187/190

(c) 188/190

(d) 18/^{20}C_{3}

## Answer

B

**Question: A letter is taken out at random from ‘ASSISTANT’ and another is taken out from ‘STATISTICS’. The probability that they are the same letters is**

(a) 1/45

(b) 13/90

(c) 19/90

(d) None of these

## Answer

C

**Question: A single letter is selected at random from the word ‘PROBABILITY’. The probability that it is a vowel is**

(a) 1/3

(b) 4/11

(c) 2/11

(d) 3/11

## Answer

A

**Question: While shuffling a pack of 52 playing cards, 2 are accidentally dropped. Find the probability that the missing cards to be of different colours.**

(a) 29/52

(b) 1/2

(c) 26/51

(d) 27/51

## Answer

C

**Question: A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour, is**

(a) 5/108

(b) 18/108

(c) 30/108

(d) 48/108

## Answer

D

**Question: Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is **

(a) 1/3

(b) 1/6

(c) 2/7

(d) 1/2

## Answer

C

**Question: If the letters of the word ALGORITHM are arranged at random in a row, what is the probability the letters GOR must remain together as a unit? **

(a) 3/72

(b) 1/72

(c) 5/72

(d) 7/72

## Answer

B

**Question: Among 15 players, 8 are batsmen and 7 are bowlers.****The probability that a team is chosen of 6 batsmen and 5 bowlers, is**

(a) ^{8}C_{6 }x ^{7}C_{5}

(b) ^{8}C_{6} +^{7}C_{5}/^{15} C _{11}

(c) 15/28

(d) None of these

## Answer

A

**Question: There are 10 prizes, five A’s, three B’s and two C’s, placed in identical sealed envelopes for the top 10 contestants in a Mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8th contestant goes to select the prize, the****probability that the remaining three prizes are one A, one B and one C is**

(a) 1/4

(b) 1/3

(c) 1/12

(d) 1/10

## Answer

A

**Question: Two cards are drawn without replacement from a well-shuffled pack. The probability that one of them is an ace of heart, is**

(a) 1/25

(b) 1/26

(c) 1/52

(d) None of these

## Answer

B

**Question: If a committee of 3 is to be chosen from a group of 38 people of which you are a member. What is the probability that you will be on the committee?**

(a) (38C_{3})

(b) (37C_{2})

(c) (37C_{2})/38C_{3})

(d) 666/8436

## Answer

C

**Question: One urn contains two black balls (labelled B _{1} and B_{2}“) and one white ball. A second urn contains one black ball and two white balls (labelled W_{1} and W_{2}).**

**Suppose, the following experiment is performed.**

**One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are chosen?**

(a) 2/3

(b) 1/3

(c) 2/5

(d) None of these

## Answer

A

**Question: In a lottery three were 90 tickets numbered 1 to 90.****Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89, is**

(a) 2/801

(b) 2/623

(c) 1/267

(d) 1/623

## Answer

A

**Question: In a certain lottery 10000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize, if you buy two tickets?**

(a)9090C_{2}/10000C_{2}

(b)9990C_{2}/10000C_{2}

(c)9900C_{2}/10000 C_{2 }

## Answer

B

**Question: A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is**

(a) 24/144

(b) 56/144

(c) 68/144

(d) 76/144

## Answer

D

**Question: Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is**

(a) 14/29

(b) 16/29

(c) 15/29

(d) 10/29

## Answer

C

**Question. A three digit number, which is a multiple of 11, is chosen at random. Probability that the number so chosen is also a multiple of 9, is equal to**

(a) 1/9

(b) 2/9

(c) 1/100

(d) 9/100

## Answer

D

**Question. A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour, is**

(a) 5/108

(b) 18/108

(c) 30/108

(d) 48/108

## Answer

D

**Question. If the letters of the word ALGORITHM are arranged at random in a row, what is the probability the letters GOR must remain together as a unit?**

(a) 3 /72

(b) 1/72

(c) 5/72

(d) 7/72

## Answer

B

**Question. If P(A) = 1 / 3, P(B) = 1 / 2 and P(A ∪ B) = 5/6, then events A and B are**

(a) mutually exclusive

(b) independent as well as mutually exhaustive

(c) independent

(d) dependent only on A

## Answer

A

**Question. Among 15 players, 8 are batsmen and 7 are bowlers. **

The probability that a team is chosen of 6 batsmen and 5 bowlers, is

(a)^{ 8}C_{6} X ^{7}C_{5} / ^{15}C_{11}

(b) ^{8}C_{6} + ^{7}C_{5} / ^{15}C_{11}

(c) 15/28

(d) None of these

## Answer

A

**Question. If P (A ∪ B) = P (A ∪ B) for any two events A and B,then**

(a) P (A) = P (B)

(b) P (A) > P (B)

(c) P (A) < P (B)

(d) None of these

## Answer

A

**Question. Two cards are drawn without replacement from a well-shuffled pack. The probability that one of them is an ace of heart, is**

(a) 1/25

(b) 1/26

(c) 1/52

(d) None of these

## Answer

B

**Question. In a certain lottery 10000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize, if you buy two tickets?**

(a) ^{9090}C_{2} /^{10000}C_{2}

(b) ^{9090}C_{2} /^{10000}C_{2}

(c) ^{9900}C_{2}/^{10000}C_{2}

(d) None of these

## Answer

B

**Question. One urn contains two black balls (labelled B1 and B2) and one white ball. A second urn contains one black ball and two white balls (labelled W1 and W2).****Suppose, the following experiment is performed.****One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then, a second ball is chosen at random from the same urn without replacing the first ball. What is the probability that two balls of opposite colour are chosen?**

(a) 2/3

(b) 1/3

(c) 2/5

(d) None of these

## Answer

A

**Question. A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is**

(a) 8/25

(b) 2/5

(c) 3/5

(d) 21/25

## Answer

B

**Question. Given, P(A) = 3/5 and P(B) = 1/5 . Find P(A or B), if A and B are mutually exclusive events. **

(a) 2/5

(b) 3/5

(c) 4/5

(d) 1/5

## Answer

C

**Question. Thirty two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players, the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is**

(a) 16/31

(b) 1/2

(c) 17/31

(d) None of these

## Answer

A

**Question. The probability of solving a question by three students are 1/2, 1/4, 1/6, respectively. Probability of question being solved will be**

(a) 33/48

(b) 35/48

(c) 31/48

(d) 37/48

## Answer

A

**Question. In a lottery three were 90 tickets numbered 1 to 90.****Five tickets were drawn at random. The probability that two of the tickets drawn numbers 15 and 89, is**

(a) 2/801

(b) 2/623

(c) 1/267

(d) 1/623

## Answer

A

**Question. Three ships A, Band C sail fromEngland 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**

(a) 18/595

(b) 6/17

(c) 3/10

(d) 2/7

## Answer

A

**Question. A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is**

(a) 24/144

(b) 56/144

(c) 68/144

(d) 76/144

## Answer

D

**Question. Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is**

(a) 14/29

(b) 16/29

(c) 15/29

(d) 10/29

## Answer

C

**Question. There are 10 prizes, five A’s, th ree B¢s and two C’s, placed in identical sealed envelopes for the top1 0 contestants in a Mathematics contest. The prizesare awarded by allowing winners to select anenvelope at random from those remaining. When the8th contestant goes to select the prize, the probability that the remaining three prizes are one A, one B and one C is**

(a) 1/4

(b) 1/3

(c) 1/12

(d) 1/10

## Answer

A

**Question. Suppose an integer from 1 through 1000 is chosen at random, find the probability that the integer is a multiple of 2 or a multiple of 9.**

(a) 0.556

(b) 0.557

(c) 0.559

(d) None of these

## Answer

A

**Question. Given two events A and B. If odds against A are as 2 : 1 and those in favour of A ∪ B are as 3 : 1, then**

(a) 1/2 ≤ P(B) ≤ 3/4

(b) 5/12 ≤ P(B) ≤ 3/4

(c) 1/4 ≤ P(B) ≤ 3/5

(d) None of these

## Answer

B

**Question. In shuffling a pack of playing cards, four are accidently dropped. The probability that missing cards should be one from each suit, is**

(a) 1/256

(b) 1/270725

(c) 2197/20825

(d) None of these

## Answer

C

**Question. In class XI of a school, 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology. **

(a) 0.5

(b) 0.6

(c) 0.65

(d) None of these

## Answer

B

**Question. If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is : **

(a) 965 /2^{11}

(b) 965/2^{10}

(c) 945/2^{10}

(d) 945/2^{11}

## Answer

C

**Question. If three of the six vertices of a regular hexa on are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :**

(a) 1/10

(b) 1/5

(c) 3/10

(d) 3/20

## Answer

A

**Question. If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :**

(a) 220(1/3)^{12}

(b) 220(1/3)^{11}

(c) 55/3(2/3)^{11}

(d) 55(2/3)^{10}

## Answer

C

**Question. If A and B are two events such that P(A∪B) = P(A∩B) , then the incorrect statement amongst the following statements is:**

(a) A and B are equally likely

(b) P(A∩B’) = 0

(c) P(A’∩B) = 0

(d) P(A) + P(B) = 1

## Answer

D

**Question. A letter is selected at random from the word ASSASSINATION. Find the probability that letter is (i) a vowel (ii) a consonant.**

(a) 5/11 , 7/11

(b) 6/13 , 6/13

(c) 6/13 , 7/13

(d) 6/11 , 7/11

## Answer

C

**Question. In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a students is selected at random and is found to be studying Mathematics.****The probability that the student is a girl is**

(a) 1/6

(b) 3/8

(c) 5/8

(d) 5/6

## Answer

B

**Question. If birth to a male child and birth to a female child are equal probable, then what is the probability that atleast one of the three children born to a couple is male ?**

(a) 4/5

(b) 7/8

(c) 8/7

(d) 1/2

## Answer

B

**Question. 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 number is less than 4, is**

(a) 1/15

(b) 14/15

(c) 1/5

(d) 4/5

## Answer

D

**Question. A five digit number is chosen at random. The probability that all the digit are distinct and digits at odd places are odd and digits at even place are even, is**

(a) 1/60

(b) 2/75

(c) 1/50

(d) 1/75

## Answer

D

**Question. A and Btoss a coin alternately till one of them tosses heads and wins the game, their respective probability of winning are**

(a) 1/4 and 3/4

(b) 1/2 and 1/2

(c) 1/3 and 3/4

(d) 1/5 and 4/5

## Answer

C

**Question. The probability that a leap year will have 53 Fridays or 53 Saturdays, is**

(a) 2/7

(b) 3/7

(c) 4/7

(d) 1/7

## Answer

B

**Question. In a non-leap year, the probability of having 53 Tuesdays or 53 Wednesdays is **

(a) 1/7

(b) 2/7

(c) 3/7

(d) None of these

## Answer

B

**Question. The probability thata50yr oldmanwillbealive at 60 is 0.83 and the probability that a 45 yr old woman will be alive at 55 is 0.87. Then, **

(a) the probability that both will be alive is 0.7221

(b) atleast one of them will alive is 0.9779

(c) atleast one of them will alive is 0.8230

(d) the probability that both will be alive is 0.6320

## Answer

(A,B)

**Question. The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are **

(a) p1 = 1/9

(b) p1 = 1/16

(c) p2 = 1/3

(d) p2 = 1/4

## Answer

(A,C)

**Question. 6 boys and 6 girls sit in a row randomly. The probability that all 6 girls sit together, is**

(a) 1/64

(b) 1/8

(c) 1/132

(d) None of these

## Answer

C

**Question. If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is :**

(a) 1/21

(b) 1/27

(c) 1/15

(d) 1/26

## Answer

B

**Question. A number x is chosen at random from the set {1, 2, 3, 4, …., 100}. Define the event: A = the chosen number x satisfies (x – 10)(x – 50)/(x – 30) ≥Then P (A) is: **

(a) 0.71

(b) 0.70

(c) 0.51

(d) 0.20

## Answer

A

**Question. Three coins are tossed together, then the probability of getting atleast one head is**

(a) 1/2

(b) 3/4

(c) 1/8

(d) 2/8

## Answer

D

We hope the above MCQ Questions Class 11 Mathematics Probability with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Probability is an important chapter in Class 11 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 11 students. Please go through these and let us know if you have any feedback in the comments section.