Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = . (ii) The probability of an event that cannot happen is . Such an event is called . (iii) The probability of an event that is certain to happen is . Such an event is called . (iv) The sum of the probabilities of all the elementary events of an experiment is . (v) The probability of an event is greater than or equal to and less than or equal to .
Step-by-Step Solution
Key Concept: Use the basic definitions of probability as given in the NCERT textbook: (a) Complementary events, (b) Impossible and certain events, (c) Exhaustive set of elementary events, and (d) Range of probability values (0 ≤ P ≤ 1).
1. Complementary events – For any event \(E\) and its complement \(E'\) ("not E"), the two together cover the whole sample space. Hence, \[P(E) + P(E') = 1.\]
2. Impossible event – An event that cannot occur has probability zero. Such an event is called an *impossible event*.
\[P(\text{impossible event}) = 0.\]
3. Certain event – An event that is sure to occur has probability one. Such an event is called a *certain event*.
\[P(\text{certain event}) = 1.\]
4. Elementary events – The set of all elementary (or simple) events of an experiment is exhaustive; their probabilities add up to the total probability of the sample space, which is 1.
\[\sum_{i=1}^{n} P(E_i) = 1,\] where \(E_i\) are the elementary events.
5. Range of probability – By definition, probability of any event lies between 0 and 1 inclusive.
\[0 \le P(A) \le 1.\]
These statements directly answer the blanks in the question.
Correct Answer: (i) 1 (ii) 0, impossible event (iii) 1, certain event (iv) 1 (v) 0, 1