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Probability Notes: Class 10 Maths Chapter 14
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.
(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.
(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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