# MCQs For NCERT Class 11 Mathematics Chapter 16 Probability

Please refer to the MCQ Questions for Class 11 Probability Maths Chapter 16 with Answers. The following Probability Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Probability with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

## Probability Class 11 MCQ Questions with Answers

See below Probability Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. If any four numbers are selected and they are multiplied, then the probability that the last digit will 1,3,5 or 7, is
(a) 4/625
(b) 18/625
(c) 16/625
(d) None of these

C

Question: A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
(a) {RW, WW}
(b) {RW, WW, WR}
(c) {RW, RR}
(d) None of these

B

Question: Which of the following cannot be valid assignments of probabilities for outcomes of sample space S (W1, W2, W3, W4, W5, W6, W7)?

(a) I, II
(b) I, III
(c) II, III, IV
(d) None of these

D

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

B

Question: A coin is tossed and a die is thrown. In coin, H and T occur and in die, a number from 1 to 6 may occur. The sample space is
(a) {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
(b) {1H, 2H, 3H, 4H, 5H, 6H, T1, T2, T3, T4, T5, T6}
(c) {H, T, 1, 2, 3, 4, 5, 6}
(d) None of the above

A

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

C

Question: A pair of dice thrown, if 5 appears on at least one f the dice, then the probability that the sum is 10 or greater, is
(a) 11/36
(b) 2/9
(c) 3/11
(d) 1/12

D

Question: What is the probability that when one die is thrown the number appearing on top is even?
(a) 1/6
(b) 1/3
(c) 1/2
(d) None of these

C

Question: A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of the numbers that turn up is 3.
(a) -1/12
(b) 1/12
(c) 1/3
(d) 1/4

B

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

B

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 2/3
(d) 1/5 and and 4/5

C

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

B

Question: If birth to a male child and birth to a female child are equal probable, then what is the probability that at least one of the three children born to a couple is male ?
(a) 4/5
(b) 7/8
(c) 8/7
(d) 1/2

B

Question: Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is
(a) 1/5
(b) 4/5
(c) 1/30
(d) 1/4

D

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) 8

D

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

C

Question: If any four numbers are selected and they are multiplied, then the probability that the last digit will 1,3,5 or 7, is
(a) 4/625
(b) 18/625
(c) 16/625
(d) None of these

C

Question: The probability that the same number appear on throwing three dice simultaneously, is
(a) 1/6
(b) 1/36
(c) 5/36
(d) None of these

B

Question: If a coin be tossed n times, then probability that the head comes odd times is
(a) 1/2
(b) 1/2n
(c) 1/2n-1
(d) None of these

A

Question: A die is rolled three times. The probability of getting a larger number than the previous number each time is
(a) 15/216
(b) 5/54
(c) 13/216
(d) 1/18

B

Question: A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.
(a) 5/9
(b) 4/9
(c) 2/9
(d) None of these

B

Question: Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on a selected coupon be 9, is
(a) (1/15)7
(b) (8/18)7
(c) (3/5)7
(d) None of these

C

Question: An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is
(a) 16/81
(b) 1/81
(c) 80/81
(d) 65/81

A

Question: A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss is equal to
(a) 1/2
(b) 1/32
(c) 31/32
(d) 1/5

A

Question. If the events A and B are mutually exclusive events such that P(A)= 3x+1/3 and P(B) = 1-X/4 , then the set of possible values of x lies in the interval :
(a) [0, 1]
(b) [1/3, 2/3]
(c) [-1/3, 5/9]
(d) [-7/9, 4/9]

C

Question. Let X and Y are two events such that P( X∪Y ) = P( X ∩Y ).
Statement 1: P( X ∩Y ‘) = P( X’∩Y ) = 0
Statement 2: P( X) + P(Y) = 2P( X∩Y)
(a) Statement 1 is false, Statement 2 is true.
(b) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
(c) Statement 1 is true, Statement 2 is false.
(d) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

B

Question. If a coin be tossed n times, then probability that the head comes odd times is
(a) 1/2
(b) 1/2n
(c) 1/2 n -1
(d) None of these

A

Question. A natural number x is chosen at random from the first 100 natural numbers. The probability that x+ 100/x > 50 is
(a) 1/10
(b) 11/50
(c) 11/20
(d) None of these

C

Question. If four digit numbers greater than 5000 are randomly formed from the digits 0, 1, 3, 5 and 7, what is the probability of forming number divisible by 5 when
(i) the digits are repeated ?
(ii) the repetition of digits is not allowed ?
(a) 30/83 , 3/8
(b) 34 , 1
(c) 33/83 , 3/8
(d) None of these

C

Question. The probability that the same number appear on throwing three dice simultaneously, is
(a) 1/6
(b) 1/36
(c) 5/36
(d) None of these

B

Question. A die is loaded in such a way that each odd number is twice as likely to occur as each even number. Find P(G), where G is the event that a number greater than 3 occurs on a single roll of the die.
(a) 5/9
(b) 4/9
(c) 2/9
(d) None of these

B

Question. A die is rolled three times. The probability of getting a larger number than the previous number each  time is
(a) 15 /216
(b) 5/54
(c) 13/216
(d) 1/18

B

Question. The probability of having atleast one tail in 4 throws with a coin, is
(a) 15/16
(b) 1/16
(c) 1/4
(d) 1

A

Question. Afive digitnumberisformedbywriting the digits 1, 2, 3, 4, 5, in a random order without repetitions.
Then, the probability that the number is divisible by 4, is
(a) 3/5
(b) 18/5
(c) 1/5
(d) 6/5

C

Question. Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that atleast one letter is in its proper  envelope.
(a) 1/3
(b) 2/3
(c) 1/5
(d) None of these

B

Question. An insurance salesman sells policies to 5 men, all of identical age and in good health. The probability that a man of this particular age will be alive after 30 yr is 2/3. The probability that after the lapse of 30 yr all the five persons will be alive, is
(a) 1/16
(b) 16/81
(c) 32/243
(d) None of these

C

Question. Twenty five coins are tossed simultaneously. The probability that the fifth coin will fall with head upwards, is
(a) 5/25
(b) 5/225
(c) 1/2
(d) None of these

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

C

(Q. Nos. 10-12) In an objective paper, there are two sections of 10 questions each. For ‘section 1’, each question has five options and only one option is correct and ‘section 2’ has four options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in ‘section 1’ is 1 and in ‘section 2’ is 3. (There is no negative marking.)
10. If a candidate attempts only two questions by guessing, one from ‘section 1’ and one from ‘section  2’, the probability that he scores in both questions is
(a) 74/75
(b) 1/25
(c) 1/15
(d) 1/75

D

Question. Let A and B be two events such that P(A ∪ B) =1/6, P(A ∪ B) = 1/4 and P(A̅) =1/4 where A stands for complement of event A. Then, events A and B are
(a) mutually exclusive and independent
(b) independent but not equally likely
(c) equally likely but not independent
(d) equally likely and mutually exclusive

B

Question. If a candidate in total attempts four questions all by guessing, then the probability of scoring 10 marks is (a) 1/15 (1/15)3
(b) 4/15 (1/15)3
(c) (1/15 ) (14/15)3
(d) None of these

B

Question. The accompanying Venn diagram shows three events, A, B and C and also the probabilities of the various intersections [for instance, P (A ∩ B) = .07].
Find P (B∩C) and probability of exactly one of the three occurs.

(a) 0.15, 0.15
(b) 0.15, 0.51
(c) 0.15, 0.50
(d) None of these

B

Question. From the employees of a company, 5 persons are selected to represent them in managing committee of the company. Particulars of five persons are as follows

A person is selected at random from this group to act as a spokes person. What is the probability that the spokes person will be either male or over 35 yr?
(a) 4/5
(b) 1/5
(c) 3/5
(d) None of these

A

Question. If P(A ∩ B) = 1/3 , P(A ∪ B) = 5/6 and P(A) = 1/2 , then which one of the following is correct?
(a) A and B are independent events
(b) A and B are mutually exclusive events
(c) P(A) = P(B)
(d) None of the above

A

Question. If A and B are arbitrary events, then
(a) P(A ∩ B) ≥ P(A) + P(B)
(b) P(A ∪ B) ≤ P(A) + P(B)
(c) P(A ∩ B) = P(A) + P(B)
(d) None of these

B

Question. An experiment yields 3 mutually exclusive and exhaustive events A, Band C. If P(A) = 2P(B) = 3P(C), then P(A) is equal to
(a) 1/11
(b) 2/11
(c) 3/11
(d) 6/11

D

Question. If the probabilities for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is [NCERT Exemplar]
(a) >.5
(b) .5
(c) ≤ .5
(d) 0

B

Question. The probability that atleast one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then P (A) + P(B) is
(a) 0.4
(b) 0.8
(c) 1.2
(d) 1.6

C

Question. If A and B are events of the same experiments with P(A) = 0.2, P(B) = 0.5, then maximum value of P(A’∩ B) is
(a) 0.2
(b) 0.5
(c) 0.63
(d) 0.25

B

Question. A man and his wife appear for an interview for two posts. The probability of the man’s selection is 1/5 and that of his wife’s selection is 1/7. The probability that atleast one of them is selected, is
(a) 9/35
(b) 12/35
(c) 2/7
(d) 11/35

D

Question. Given two mutually exclusive events A and B such that P(A) = 0.45 and P(B) = 0.35, P(A ∩ B) is equal to
(a) 63/400
(b) 0.8
(c) 63/200
(d) 0

A

Question. Three letters are written to there different persons and addresses on the three envelopes are also written. Without looking at the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is
(a) 1/2
(b) 1/3
(c) 1/6
(d) 5/6

B

Question. A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that I. All the three balls are white
II. All the three balls are red
III. One ball is red and two balls are white
I          II        III
(a) 5/143 , 29/143, 40/143
(b) 5/143 , 28/143, 40/143
(c) 7/143 , 28/143, 40/143
(d) None of the above

B

Question. An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn.
The probability that the three balls have different colours, is
(a) 1/3
(b) 2/7
(c) 1/21
(d) 2/23

B

Question. A die is thrown. Let A be the event that the number obtained is greater than 3 and B be the event that the number obtained is less than 5. Then, P (A ∪ B) is
(a) 2/5
(b) 3/5
(c) 0
(d) 1

D

Question. 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) 5/128
(b) 25/128
(c) 5/512
(d) None of the above

C

Question. If A and B are two events such that P(A) = 3/ 4 and P(B) = 5/8, then
(a) P (A È B) ³ 3/4
(b) P (A¢ Ç B) £ 1/4
(c) 3/8 £ P (A Ç B) £ 5/8
(d) None of the above

(A,B,C)

Question. The probability of getting a score less than 40 by answering all the questions by guessing in this paper is
(a) (1 /75)10
(b) 1 – (1/75 )10
(c) (74/75)10
(d) None of these

B

Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

D

Question. Statement I 20 persons are sitting in a row. Two of these persons are selected at random. The probability that two selected persons are not together is 0.7.
Statement II If A is an event, then P(not A) = 1 – P(A).

D

Question. Statement I If A and B are two events such that P(A) = 1/2 and P(B) = 2/3 , then 1/6 ≤ P(A∩B)≤ 1/2
Statement II P(A ∪ B) ≤ max {P(A), P(B)} and P(A ∩ B) ³ min {P(A), P(B)}.

C

Question. Statement I If A, B, C be three mutually independent events, then A and B ∪C are also independent events.
Statement II Two events A and B are independent if and only if P(A ∩ B) = P(A) P(B).

A

Question. Statement I The probability of drawing either an ace or a king from a pack of card in a single draw is 2/13.
Statement II For two events A and B which are not mutually exclusive,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B).

A

Question. Two aeroplanes I and II bomb a target in succession.
The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only, if the first misses the target. The probability that the target is hit by the second plane, is
(a) 0.06
(b) 0.14
(c) 0.32
(d) 0.7

C

In an objective paper, there are two sections of 10 questions each. For ‘section 1’, each question has five options and only one option is correct and ‘section 2’ has four options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in ‘section 1’ is 1 and in ‘section 2’ is 3.

Question: If a candidate in total attempts four questions all by guessing, then the probability of scoring 10 marks is
(a) 1/15 (1/(15)3
(b) 4/5 (1/15)3
(c) 1/15 (14/15)3
(d) None of these

B

Question: If a candidate attempts only two questions by guessing, one from ‘section 1’ and one from ‘section 2’, the probability that he scores in both questions is
(a) 74/75
(b) 1/25
(c) 1/15
(d) 1/75

D

Question: The probability of getting a score less than 40 by answering all the questions by guessing in this paper is
(a) (1 /75) 10
(b) 1 1 75 10
(c) (74/75) 10
(d) None of these

D

Assertion and Reason
Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the
correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question: Statement I If A and B  are two events such that P (A ) =1/2 and P(B) = 2/3, then 1/6 ≤ P(A∩B) ≤1/2.
Statement II P(A∪(B)≤ max{P(A), P(B)} and P(A∩B)≥ Min{P(A), P(B)}

C

Question: Statement I If A, B, C  be three mutually independent events, then A and B∪C are also independent events.
Statement II Two events A and B are independent if and only if P( A∩B) =p(A)P(B).

A

Question: Statement I 20 persons are sitting in a row. Two of these persons are selected at random. The probability that two selected persons are not together is 0.7.
Statement II If A is an event, then P(not A= 1-P(A).

D

Question: An urn contains nine balls of which three are red,four are blue and two are green. Three balls are drawn at random without replacement from the urn.
The probability that the three balls have different colours, is
(a) 1/3
(b) 2/7
(c) 1/21
(d) 2/23

B

Question: Statement I The probability of drawing either an ace or a king from a pack of card in a single draw is 2/13.
Statement II For two events A and B which are not mutually exclusive, P(A∪B) = P(A) + P(B)-P(A∩B).

A

Question: Two aeroplanes I and II bomb a target in succession.
The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only, if the first misses the target. The probability that the target is hit by the second plane, is
(a) 0.06
(b) 0.14
(c) 0.32
(d) 0.7

C

Question: A die is thrown. Let A be the event that the number obtained is greater than 3 and B be the event that the number obtained is less than 5. Then, P (A ∪ B) is
(a) 2/5
(b) 3/5
(c) 0
(d) 1

D

Question: Let A and B be two events such that

A B and are
(a) mutually exclusive and independent
(b) independent but not equally likely
(c) equally likely but not independent
(d) equally likely and mutually exclusive