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NCERT Solutions for Class 10 Maths Chapter 14 Probability

NCERT Solutions for Class 10 Maths Chapter 14 Probability covers the theoretical (classical) approach to probability, based on equally likely outcomes of a random experiment.

Overview of Topics & Subtopics (Click to Jump)

1. Theoretical (Classical) Probability

Short Note:

• Theoretical Probability of an event E, P(E) = (Number of outcomes favourable to E) / (Total number of possible outcomes), assuming all outcomes are equally likely.

• 0 ≤ P(E) ≤ 1. P(sure event) = 1. P(impossible event) = 0.

• For any event E, P(E) + P(not E) = 1, i.e., P(E) + P(E') = 1, where E' is the complement of E.

2. Common Random Experiments

Short Note:

• Coin toss: 2 equally likely outcomes (Head, Tail).

• Single die throw: 6 equally likely outcomes (1 to 6).

• Deck of playing cards: 52 cards in 4 suits (13 each of spades, hearts, diamonds, clubs), with 12 face cards in total.

NCERT Textbook Exercise Questions

A coin is tossed once. Find the probability of getting a tail.
Answer: Total outcomes = 2 (H, T). Favourable outcomes for tail = 1. P(tail) = 1/2.
A die is thrown once. Find the probability of getting (i) a prime number, (ii) a number greater than 4.
Answer: (i) Prime numbers on a die: 2, 3, 5 ⇒ 3 outcomes. P = 3/6 = 1/2.
(ii) Numbers greater than 4: 5, 6 ⇒ 2 outcomes. P = 2/6 = 1/3.
A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that the card is (i) a king, (ii) a face card.
Answer: (i) There are 4 kings. P(king) = 4/52 = 1/13.
(ii) There are 12 face cards (4 each of jack, queen, king). P(face card) = 12/52 = 3/13.
Two dice are thrown simultaneously. Find the probability of getting a sum of 8.
Answer: Total outcomes = 36. Outcomes giving sum 8: (2,6),(3,5),(4,4),(5,3),(6,2) ⇒ 5 outcomes. P(sum=8) = 5/36.
A bag contains 3 red balls and 5 black balls. A ball is drawn at random. Find the probability that the ball drawn is (i) red, (ii) not red.
Answer: Total balls = 8. (i) P(red) = 3/8. (ii) P(not red) = 1 − 3/8 = 5/8.
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More for this chapter

Class 10 › Mathematics › Probability
Chapter notesRead the chapterPractice MCQsCheck what you rememberChapter test10 questions on one pageOnline testTest 1, 2 and 3, one question at a timePYQPrevious year questionsStudy materialPDF notes
Topics in this chapter: Theoretical (Classical) ProbabilityCommon Random Experiments