15 Probability
1. The probability of an event is P(E). Which of the following is true?
(a) 0 P(E) 1 (b) 0 < P(E) < 1
(c) –1 P(E) 1 (d) –1 P(E) < 1
2. Which of the following is true for an event (E)?
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(a) P( E ) = 1 + P(E) (b) P(E) = 1 + P( E )
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(c) P(E) + P( E ) =1 (d) P(E) – P( E ) = –1
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3. The sum of the probabilities of all the elementary events of an experiment is
d.
(a) 0 (b) 1 (c) –1 (d) none of these
4. The events which have equal chances to occur or no one is preferred over the other are
called
(a) impossible events (b) equally likely events
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(c) certain / sure events (d) none of these
5. The probability of an event that cannot happen is ______ . Such an event is called
a/an ______ .
(a) 1, sure event (b) 0, certain event
(c) 0, impossible event (d) none of these
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6. If A is an event of a random experiment, then Ac or A is called the _____ of the event.
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(a) complement (b) mutually exclusive
(c) elementary (d) none of these
7. When sum of the probabilities of two events is 1, the events are called
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(a) elementary events (b) mutually exclusive events
(c) complementary events (d) all of these
8. An outcome of a random experiment is called a/an
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(a) elementary event (b) sure event
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(c) complementary event (d) impossible event
MATHEMATICS-10 1
9. Which one of the following is true for an event (E)?
Number of trials in which the event happened
(a) P(E) Total number of trials
Number of trials in which the event happened
(b) P(E) Total number of trials
Number of outcomes favourable to E
(c) P(E) Number of all possible outcomes of the experiment
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(d) both (b) and (c) are correct.
10. Two coins are tossed simultaneously. The probability of getting atmost one head is
t. d
1 1 3
(a) (b) (c) (d) 1
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d.
4 2 4
11. A fair die is thrown once. The probability of getting a composite number less than 5 is
1 1 2
(a) (b) (c) (d) 0
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12. If in a lottery, there are 5 prizes and 20 blanks, then the probability of getting a prize is
2 4 1
(a) (b) (c) (d) 1
5 5 5
13. If a number x is chosen from the numbers –2, –1, 0, 1, 2,
then, the probability that x2 < 2 is
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2 4 1 3
(a) (b) (c) (d)
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5 5 5 5
14. Which of the following relationships is/are correct?
(a) P(E) + P( E ) = 1 (b) 0 P( E ) 1
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(c) 0 P(E) 1 (d) all of these
15. A die is thrown twice. The probability of getting 4,5 or 6 in the first throw is
1 2 1 1
(a) (b) (c) (d)
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3 3 2 4
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16. A letter is chosen at random from the letters of the word ‘ASSASSINATION’. If the
6
probability that the letter chosen is a vowel is in the form of , then x is equal to
2x 1
(a) 5 (b) 6 (c) 7 (d) 8
17. A number x is selected from the numbers 1, 2, 3 and then a second number y is randomly
selected from the numbers 1, 4, 9 then the probability that the product xy of the two
numbers will be less than 9 is
3 4 5 7
(a) (b) (c) (d)
7 9 9 9
2 MATHEMATICS-10
18. If odds in against of an event be 3 : 8, then the probability of occurrence of this event is
3 5 3 8
(a) (b) (c) (d)
8 8 11 11
19. A bag contains 8 red balls and some blue balls. If the probability of drawing a blue ball
is three times of a red ball, then the number of blue balls in the bag is
(a) 12 (b) 18 (c) 24 (d) 36
20. There are 1000 sealed envelopes in a box. 10 of them contain a cash prize of < 100 each,
100 of them contain a cash prize of < 50 each and 200 of them contain a cash prize of
< 10 each and rest do not contain any cash prize. If they are well-shuffled and an envelope
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is picked up out, then the probability that it contains no cash prize is
(a) 0.65 (b) 0.69 (c) 0.54 (d) 0.57
t. d
21. A helicopter was crashed somewhere in the region given below.
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d.
D C
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A 10 km B
The probability that the helicopter was crashed in the shaded region is
(a) 0.75 (b) 0.57 (c) 0.61 (d) 0.77
22. The experimental probability of an event is equal to its theoretical probability, if the
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number of trials of an experiment is
(a) small (b) large (c) very large (d) very small
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23. Which of the following cannot be the probability of an event?
1 17
(a) (b) 0.1 (c) 3% (d)
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3 16
24. An event is very unlikely to happen. Its probability is closest to
(a) 0.0001 (b) 0.001 (c) 0.01 (d) 0.1
25. The probability expressed as a percentage of a particular occurrence can never be
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(a) less than 100 (b) less than 0
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(c) greater than 1 (d) anything but a whole number
26. A bag contains 3 red balls, 5 white balls and 7 black balls. What is the probability that
a ball drawn from the bag at random will be neither red nor black?
1 1 7 8
(a) (b) (c) (d)
5 3 15 15
27. The probability of an event that is sure to happen is
(a) 0 (b) –1 (c) 1 (d) all of these
MATHEMATICS-10 3
28. The king, queen and jack of clubs are removed from a deck of 52 cards and the remaining cards
are shuffled. A card is drawn from remaining cards. The probability of getting a card of hearts is
13 3 10 14
(a) (b) (c) (d)
49 49 49 52
29. The king, queen and jack of clubs are removed from a deck of 52 cards and the remaining cards
are shuffled. A card is drawn from remaining cards. The probability of getting a card of queen is
3 13 30 7
(a) (b) (c) (d)
49 49 49 26
30. The king, queen and jack of clubs are removed from a deck of 52 cards and the remaining cards
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are shuffled. A card is drawn from remaining cards. The probability of getting a card of club is
t. d
20 10 13 12
(a) (b) (c) (d)
49 49 49 52
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d.
31. A card is drawn from a well shuffled deck of 52 playing cards, then the probability of
getting a black card is
8 16 1 4
(a) (b) (c) (d)
15 52 2 52
32.
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A card is drawn from a well shuffled deck of 52 playing cards, then the probability of
getting an ace is
40 14 1 4
(a) (b) (c) (d)
52 52 13 52
33. A card is drawn from a well shuffled deck of 52 playing cards, then the probability of getting
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a card of diamonds is
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4 1 1
(a) (b) (c) (d) none of these
52 4 13
34. A card is drawn randomly from a well shuffled deck of 52 playing cards. Then the
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probability that the card drawn is a king of red colour is
1 11 12
(a) (b) (c) (d) none of these
26 26 52
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35. A card is drawn randomly from a well shuffled deck of 52 playing cards. Then the
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probability that the card drawn is neither a spade nor a king is
13 9 34 52
(a) (b) (c) (d)
9 13 52 36
36. A card is drawn randomly from a well shuffled deck of 52 playing cards. Then the
probability that the card drawn is either a face card or a card of hearts is
11 26 11
(a) (b) 22 (c) (d)
26 11 13
4 MATHEMATICS-10
37. A card is drawn randomly from a well shuffled deck of 52 playing cards. Then the
probability that the card drawn is neither a king nor a queen is
2 12 18 11
(a) (b) (c) (d)
13 13 52 13
38. When two different dice are thrown at the same time, the number of possible outcomes is
(a) 6 × 6 = 36 (b) 6 × 5 = 30 (c) 38 (d) none of these
39. When two different dice are thrown at the same time, the probability of getting a doublet is
1 1
(a) (b) 1 (c) (d) 0
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12 6
40. When two dice are thrown at the same time, the probability of getting a product, which
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is a perfect square is
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4 2 1 1
d.
(a) (b) (c) (d)
9 9 18 12
41. What is the probability that a number selected from the numbers 1 to 25 is not a prime
number when each of the given numbers is equally likely to be selected?
16 17 4 25
ns Kid
(a)
25
(b)
16
(c)
52
(d)
16
42. A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What
is the probability that this bulb is defective?
5 20 15 1
(a) (b) (c) (d)
20 4 19 5
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43. A lot of 20 bulbs contain 4 defective ones. One bulb drawn at random from the lot.
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Suppose the bulb drawn is not defective and is not replaced. Now one bulb is drawn at
random from the rest. What is the probability that this bulb is not defective?
15 19
(a) 19 (b) 15 (c) (d)
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19 15
44. A lot consists of 144 ball pens of which 20 are defective and others are good. Nuri will buy
a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at
random and gives it to her. What is the probability that she will not buy it?
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5 5 124
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(a) (b) (c) (d) none of these
31 36 144
45. Savita and Hamida are friends. What is the probability that both will have different
birthdays? (ignoring a leap year)
364 363 364 1
(a) (b) (c) (d)
365 365 366 365
46. Savita and Hamida are friends. What is the probability that both will have the same
birthday? (ignoring a leap year)
1 – 364 363 1
(a) (b) (c) (d) none of these
365 365 365
MATHEMATICS-10 5
47. A piggy bank contains hundred 50p coins, fifty 1 coins, twenty 2 coins and ten 5 coins.
If it is equally likely that one of the coins will fall out when the bank is turned upside down,
what is the probability that the coin will be a 50p coin?
5 5 9
(a) (b) (c) (d) none of these
90 9 90
48. A piggy bank contains hundred 50p coins, fifty 1 coins, twenty 2 coins and ten 5 coins.
If it is equally likely that one of the coins will fall out when the bank is turned upside down,
what is the probability that the coin will not be a 5 coin?
1 5 17 18
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(a) (b) (c) (d)
18 9 18 17
49. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random
t. d
from the box, then the probability that it bears a two digit number is
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d.
1 1 9 81
(a) (b) (c) (d)
90 10 10 10
50. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random
from the box, then the probability that it bears a perfect square number is
1 1
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(a) 10 (b)
10
(c) 9 (d)
9
51. Five cards-the ten, jack, queen, king and ace of diamonds, are well shuffled with their face
downwards.
One card is then picked up at random. If the queen is drawn and put aside, what is the
probability that the second card picked up is an ace?
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1
(a) 4 (b) (c) 1 (d) none of these
4
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52. Five cards-the ten, jack, queen, king and ace of diamonds, are well shuffled with their face
downwards.
One card is then picked up at random. If the queen is drawn and put aside, what is the
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probability that the second card picked up is a queen?
1
(a) 0 (b) 4 (c) (d) 5
5
53. Three coins are tossed simultaneously. Then the probability of getting all tails or no head is
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1
(a) (b) 7 (c) 17 (d)
8
54. Three coins are tossed simultaneously. Then the probability of getting exactly two heads
is
8 3 7 4
(a) (b) (c) (d)
3 8 8 8
55. Three coins are tossed simultaneously. Then the probability of getting at most two tails is
3 8 7
(a) (b) (c) (d) 8
8 7 8
6 MATHEMATICS-10
56. A game of chance consists of spinning on arrow which comes to rest pointing at one of the
numbers 1, 2, 3, 4, 5, 6, 7, 8 and there are equal likely outcomes. Then what will be the
probability that it will point at a number greater than 2?
8 1
7 2
6 3
5 4
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3 4 2
t. d
(a) (b) (c) (d) none of these
4 8 8
57. One card is drawn from a well shuffled deck of 52 cards. Then the probability of getting
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d.
the jack of spades is ______ .
1 13 4
(a) (b) (c) (d) none of these
52 52 52
58. Two coins are tossed simultaneously, then the probability of getting at least one head is
ns Kid
4 3 3
(a) (b) (c) (d) none of these
3 4 7
59. Amit drawn a card from a well shuffled deck of 52 cards. What is the probability that he
drawn an eight is
1 13 1
(a) (b) (c) (d) none of these
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52 52 13
60. Amit drawn a card from a well shuffled deck of 52 cards. What is the probability that he
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drawn a spade?
4 1 1 3
(a) (b) (c) (d)
52 4 2 52
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61. Amit drawn a card from a well shuffled deck of 52 cards. What is the probability that he
drawn the six of the clubs?
3 4 1
(a) (b) (c) 52 (d)
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52 52 52
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62. One card is drawn from a well shuffled deck of 52 cards. Then the probability of getting
a queen of black suit is
1 1 3 13
(a) (b) (c) (d)
26 52 26 52
63. 17 cards numbered 1, 2, 3, ... , 17 are put in a box and mixed thoroughly. One person draws
a card from the box. The probability of getting a prime number on the card is
7 6 5 7
(a) (b) (c) (d)
16 17 16 17
MATHEMATICS-10 7
64. In a single throw of two dice, the probability of getting a total of 8 is
5 36 50 13
(a) (b) (c) (d)
36 5 36 52
65. Two dice are thrown at the same time. Then the probability of getting different numbers
on both dice is
1 1 1
(a) 1 (b) 1– (c) (d)
6 6 36
66. The experiments which when repeated under identical conditions produce the same
results or outcomes are known as
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(a) random experiments (b) probability experiment
t. d
(c) elementary experiment (d) deterministic experiment
67. The set of all possible outcomes of a random experiment is called
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d.
(a)sample space (b) elementary events
(c) complementary events (d) favourable events
68. The probability of a non-leap year having 53 Mondays is
1 4 1
(a) 7 (b) (c) (d)
7 45 53
69.
ns Kid
20 tickets, on which numbers 1 to 20 are written, are mixed thoroughly and then a ticket
is drawn at random out of them. Then the probability that the number on the drawn ticket
is a multiple of 3 or 7 is
8 3 7 2
(a) (b) (c) (d)
19 7 3 5
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70. A number is chosen at random from the numbers –3, –2, –1, 0, 1, 2, 3. What will be the
probability that square of this number is less than or equal to 1?
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7 3 7 2
(a) (b) (c) (d)
52 7 3 5
71. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look
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at a pen and tell whether or not it is defective. One pen is taken out at random from this
lot, the probability that the pen taken out is a good one is
12 11 133 11
(a) (b) (c) (d)
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11 12 144 132
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72. A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is
selected at random from the numbers 1, 4, 9 and 16. The probability that product of x and
y is less than 16 is
2 1 1 4
(a) (b) (c) (d)
11 3 2 16
73. What is the probability that in a leap year there will be 53 Tuesdays?
2 1 7
(a) 2 (b) (c) (d)
7 7 2
8 MATHEMATICS-10
a
74. In the figure, a disc is shown on which a player spins an arrow twice. The function is
b
formed, where ‘a’ is the number of sector on which arrow stops on the first spin and ‘b’
is the number of the sector in which the arrow stops on second spin.
2
3 1
4 6
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5
t. d
On each spin, each sector has equal chance of selection by the arrow. Then the probability
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d.
a
that the fraction >1 is
b
15 5 5
(a) (b) (c) (d) none of these
12 36 12
75.
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Probability of event can never be
(a) positive (b) negative (c) greater than 0 (d) none of these
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MATHEMATICS-10 9
Answers
1. (a) 2. (c) 3. (b) 4. (b) 5. (c) 6. (a)
7. (c) 8. (a) 9. (d) 10. (c) 11. (b) 12. (c)
13. (d) 14. (d) 15. (c) 16. (b) 17. (c) 18. (c)
19. (c) 20. (b) 21. (b) 22. (c) 23. (d) 24. (a)
25. (b) 26. (b) 27. (c) 28. (a) 29. (a) 30. (b)
31. (c) 32. (c) 33. (b) 34. (a) 35. (b) 36. (a)
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37. (d) 38. (a) 39. (c) 40. (b) 41. (a) 42. (d)
t. d
43. (c) 44. (b) 45. (a) 46. (c) 47. (b) 48. (c)
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49. (c) 50. (b) 51. (b) 52. (a) 53. (a) 54. (b)
d.
55. (c) 56. (a) 57. (a) 58. (b) 59. (c) 60. (b)
61. (d) 62. (a) 63. (d) 64. (a) 65. (b) 66. (d)
67. (a) 68. (b) 69. (d) 70. (b) 71. (b) 72. (c)
73.
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(b) 74. (c) 75. (b)
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10 MATHEMATICS-10
