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NCERT Solutions for Class 11 Math Ch-14: Probability
NCERT Solutions for Class 11 Maths Chapter 14 Probability introduces the fundamentals of random experiments, sample spaces, events, and the axiomatic approach to probability, along with rules for calculating probabilities of combined events.
Overview of Topics & Subtopics
Important Questions and Answers
Q1: What is a sample space, and what is an event in the context of probability?
Answer: A sample space is the set of all possible outcomes of a random experiment. An event is any subset of the sample space, representing one or more outcomes that satisfy a particular condition.
Q2: What are mutually exclusive events?
Answer: Two events are said to be mutually exclusive if they cannot occur simultaneously, meaning their intersection is an empty set; for example, when tossing a coin, getting a head and getting a tail are mutually exclusive events.
Q3: What is the formula for the probability of an event E under the axiomatic (classical) approach?
Answer: Under the axiomatic approach, for a sample space with equally likely outcomes, the probability of an event E is given by P(E) = n(E) / n(S), where n(E) is the number of favourable outcomes and n(S) is the total number of possible outcomes in the sample space.
Q4: State the addition rule (theorem) of probability for two events A and B.
Answer: The addition rule of probability states that P(A ∪ B) = P(A) + P(B) − P(A ∩ B). If A and B are mutually exclusive events, this simplifies to P(A ∪ B) = P(A) + P(B), since P(A ∩ B) = 0.
Q5: What is the range of possible values for the probability of any event?
Answer: The probability of any event E always lies between 0 and 1, inclusive, i.e., 0 ≤ P(E) ≤ 1, where P(E) = 0 indicates an impossible event and P(E) = 1 indicates a certain event.
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