Chapter 26. Introduction to Probability NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers
Chapter 26. Introduction to Probability | NIOS Class 10 Mathematics Important Questions, Fully Solved Answers, and Chapter-wise Exam Preparation Guide.
Chapter 26. INTRODUCTION TO PROBABILITY
Multiple Choose Questions and Answers for Introduction to Probability [1 Mark]
Question: If 
, then P(E) =
(a) 0 (b) – 1 (c) 1 (d) 0.5
Answer: (c) 1
[ Here,
We have, 
]
Question: The sum of the probabilities of all the elementary events of an experiment is ..............
(a) – 1 (b) 1 (c) 0.2 (d) 0.5
Answer: (b) 1
Question: Which of the following can not be the probability of an event?
(A) 
(B) – 1.01 (C) 12% (D) 0.3
Answer: (B) – 1.01
[ A probability always lies between 0 and 1, i.e., 
]
Question: A card is selected at random from a well shuffled deck of 52 playing cards. The probability of its being a face card is
(A) 
(B) 
(C) 
(D) 
Answer: (A)
[ The number of face cards = 12
]
Question: If an event cannot occur, then its probability is
(A) 1 (B) 
(C) 
(D) 0
Answer: (D) 0
Question: Which of the following cannot be the probability of an event?
(A) 
(B) 0.1 (C) 3% (D) 
Answer: (D)
[ We hve, 
]
Question: In a single throw of two dice, the probability of getting the sum 2 is
(A) 
(B) 
(C) 
(D) 
Answer: (C)
[ Total number of possible outcomes = 6 × 6 = 36
The number of favourable outcomes = 1 [(1,1)
]
Question: In a simultaneous toss of two coins, the probability of getting one head and one tail is
(A) 
(B) 
(C) 
(D) 
Answer: (C)
[ Total number of possible outcomes = 4 [ HH , HT , TH , TT ]
The number of favourable outcomes = 2 [HT,TH]
Therefore,
]
Question: If 
, then the probability of ‘not E’ is
(a) 
(b) 
(c) 
(d) 
Answer: (c)
[ We have, 
]
Question: If P(A) denotes the probability of an event A, then
(A) P(A) < 0 (B) P(A) > 1 (C) 0 ≤ P(A) ≤ 1 (D) –1 ≤ P(A) ≤ 1
Answer: (C) 0 ≤ P(A) ≤ 1 .
Short Questions and Answers for Introduction to Probability [1 or 2 Marks]
Question: A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that this card is a face card.
Solution: Number of all possible outcomes = 52
Number of outcomes favourable to the Event E “a face card” = 3 × 4 = 12 [Kings, queens, and jacks are face cards]
Question: A coin is tossed two times. What is the probability of getting a head each time?
Solution: The number of possible outcomes = 4 [ HH , HT , TH , TT ]
Let E be the event “getting head each time”.
Question: Two different coins are tossed at the same time. Write down all possible outcomes. What is the probability of getting head on one and tail on the other coin?
Solution: The total number of possible outcomes = 4. [HH,HT,TH,TT]
The number of outcomes favourable to the Event E “head on one and tail on the other coin” = 4 – 2 = 2 . [HT,TH]
Question: A coin is tossed once. Find the probability of getting (i) a head, (ii) a tail.
Solution: Number of possible outcomes = 2 [H,T]
(i) Let E be the event “getting a head”.
Number of outcomes favourable to E = 1 (i.e., H)
(i) Let E be the event “getting a tail”.
Number of outcomes favourable to E = 1 (i.e., T)
Question: A die is thrown once. What is the probability of getting a number 3?
Solution: Let E be the event “getting a number 3”.
Number of possible outcomes = 6 [1, 2, 3, 4, 5, 6 ]
Number of outcomes favourable to E = 1 (i.e., 3)
Question: 10 defective rings are accidentally mixed with 100 good ones in a lot. It is not possible to just look at a ring and tell whether or not it is defective. One ring is drawn at random from this lot. What is the probability of this ring to be a good one?
Solution: Number of all possible outcomes = 10 + 100 = 110
Number of outcomes favourable to the event E “ ring is good one” = 100
Long Questions and Answers for Introduction to Probability [ 3 or 4 Mark]
Question: A card is drawn from a well shuffled deck of 52 playing cards. Find the probability that it is of (i) red colour (ii) black colour
Solution: (i) Let E be the event that the card drawn is of red colour.
Number of cards of red colour = 13 + 13 = 26 [13 Diamonds and 13 Hearts]
So, the number of favourable outcomes to E = 26
Total number of cards = 52
(ii) Let F be the event that the card drawn is of black colour.
Number of cards of black colour = 13 + 13 = 26 [13 Spades and 13 Clubs ]
Question: A bag contains 3 red and 5 white balls. A ball is drawn from the bag without looking into it. What is the probability of this ball to be of (i) red colour (ii) white colour?
Solution: Total number of ball = 3 + 5 = 8 .
(i) The number of red balls = 3
(ii) The number of white balls = 5
Question: A bag contains 15 white balls and 10 blue balls. A ball is drawn at random from the bag. What is the probability of drawing
(i) a ball of not blue colour (ii) a ball not of white colour
Solution: Total number of balls = 15 + 10 = 25
(i) The number of outcomes favourable to the Event E “a ball of not blue colour” = 25 – 10 = 15 .
(ii) The number of outcomes favourable to the Event E “a ball not of white colour” = 25 – 15 = 10 .
Question: A bag contains 15 red balls and some green balls. If the probability of drawing a green ball is 
, find the number of green balls.
Solution: Let x the number of green balls .
Total number of balls 
A/Q, 
Therefore, the number of green ball is 3 .
Question: Two dice are thrown simultaneously and the sum of the numbers appearing on them is noted. What is the probability that the sum is
(a) 9 (b) 10 (c) 12
Solution: The total number of possible outcomes = 6 × 6 = 36.
The sample space = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
(a) The number of outcomes favourable to the Event E “the sum of 9” = 4 [(3,6) ,(4,5),(5,4),(6,3)] .
(b) The number of outcomes favourable to the Event E “the sum of 10” = 3 [(4,6),(5,5),(6,4)] .
(c) The number of outcomes favourable to the Event E “the sum of 12” = 1 [(6,6)] .
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