11th Mathematics NCERT Chapter 14
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– Event: A subset of the sample space
– Impossible event: The empty set
– Sure event: The whole sample space
– Complementary event or ‘not event’: The set A′ or S – A
– Event A or B: The set A ∪ B
– Event A and B: The set A ∩ B
– Event A and not B: The set A – B
– Mutually exclusive event: A and B are mutually exclusive if A ∩ B = φ
– Exhaustive and mutually exclusive events: Events E1, E2,…, En are mutually exclusive and exhaustive if E1 ∪ E2 ∪ … ∪ En = S and Ei ∩ Ej = φ V i ≠ j
– Equally likely outcomes: All outcomes with equal probability
– Probability of an event: For a finite sample space with equally likely outcomes, the probability of an event A is P(A) = n(A) / n(S), where n(A) is the number of elements in set A and n(S) is the number of elements in set S
– Probability of A or B: P(A or B) = P(A) + P(B) – P(A and B) or equivalently P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
– Probability of mutually exclusive events A and B: P(A or B) = P(A) + P(B)
– Probability of not A: P(not A) = 1 – P(A)
These are some of the key topics covered in the chapter on probability【4:0†source】.
What is the probability that atleast one tail occurs when a coin is tossed twice?
If a die is thrown, what is the probability that a prime number will appear?
From a pack of 52 cards, how many points are there in the sample space when a card is selected?
When a fair coin and a fair die are tossed, what is the probability of the sum of numbers turning up being 3?
If E and F are events with P(E) = 1/4 and P(F) = 1/2, calculate P(E and F).
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