CBSE Class 12 Mathematics Probability Assignment Set B

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
Answer : A

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. Two fair dice are tossed. 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. Three identical dice are rolled. 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 coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is:
a. 1/8
b. 1/12
c. 1/2
d. 1
Answer : B

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. 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 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. 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. If a dice is thrown twice, then the probability of getting 1 in the first throw only is:
a. 1/36
b. 3/36
c. 5/36
d. 1/6
Answer : C

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. 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 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. 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. 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. 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. 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. 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. 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 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. 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. 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. 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. 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. 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. 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. 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. 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 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 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. 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. 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. A party of 23 persons take their seats at a round table. The odds against two persons sitting together are:
a. 10 : 1
b. 1 : 11
c. 9 : 10
d. None of these
Answer : A

Question. The probability of happening at least one of the events A and B is 0.6. If the events A and B happens simultaneously with the probability 0.2, then P(A) + P(B) = ?
a.0.4
b.0.8
c.1.2
d.1.4
Answer : C

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. 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. An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is:
a. 5/1296
b. 5/1944
c. 5/2592
d. None of these
Answer : C

Question. A bag contains 3 white and 5 black balls. If one ball is drawn, then the probability that it is black, is:
a. 3/8
b. 5/8
c. 6/8 
d. 10/20
Answer : B

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. 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 is:
a. 37/60
b. 47/60
c. 1/4
d. 3/4
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. If A and B are two independent events such that P(A) = 0. 40, P(B) = 0. 50. Find P (neither A nor B)
a.0.90
b.0.10
c.0.2
d.0.3
Answer : D

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. Let A and B be two events such that P(A) = 0.3 and P(A∪ B) = 0.8. If A and B are independent events, then P(B) = ?
a. 5/6
b. 5/7
c. 3/5
d. 2/5
Answer : B

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. 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 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:
a. 0.39
b. 0.25
c. 0.904
d. None of these
Answer : A

LEVEL I

1. A bag contains 6 red and 5 blue balls and another bag contains 5 red and 8 blue balls. A ball is drawn from the first bag and without noticing its colour is put in the second bag. A ball is drawn from the second bag . Find the probability that the ball drawn is blue in colour.

2. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both hearts . Find the probability of the lost card being a heart.

3. An insurance company insured 2000 scooter and 3000 motorcycles . The probability of an accident involving scooter is 0.01 and that of motorcycle is 0.02 . An insured vehicle met with an accident. Find the probability that the accidental vehicle was a motorcycle.

4. A purse contains 2 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin.

5. Two thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting first class is 0.25 and that of a boy is getting a first class is 0.28. Find the probability that a student chosen at random will get first class marks in the subject.

LEVEL II

1. Find the probability of drawing a one-rupee coin from a purse with two compartments one of which contains 3 fifty-paise coins and 2 one-rupee coins and other contains 2 fifty-paise coins and 3 onerupee coins.

2. Suppose 5 men out of 100 and 25 women out of 1000 are good orator. An orator is chosen at random. Find the probability that a male person is selected. Assume that there are equal number of men and women.

3. A company has two plants to manufacture bicycles. The first plant manufactures 60 % of the bicycles and the second plant 40 % . Out of that 80 % of the bicycles are rated of standard quality at the first plant and 90 % of standard quality at the second plant. A bicycle is picked up at random and found to be standard quality. Find the probability that it comes from the second plant.

Please refer to attached file for CBSE Class XII Mathematics - Probability Assignment 2