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 .
Answer:
(i) Probability of an event E + Probability of the event ‘not E’ = 1
- Explanation:
Imagine you roll a die. If the event E is “rolling a 3,” then the event “not E” is “not rolling a 3.” Since either E or not E must happen, their probabilities add up to 1. If the probability of E is 0.2 (like getting a 3), the probability of not E (getting anything other than a 3) will be 0.8, and 0.2 + 0.8 = 1
(ii) The probability of an event that cannot happen is 0. Such an event is called an impossible event.
- Explanation:
An impossible event is something that can’t happen at all. For example, when rolling a regular die, the probability of rolling a 7 is 0 because a die only has numbers 1 through 6. So, the probability of rolling a 7 is impossible, and we say its probability is 0.
(iii) The probability of an event that is certain to happen is 1. Such an event is called a certain event.
- Explanation:
A certain event is something that is 100% guaranteed to happen. For example, if you roll a die, the probability of getting a number between 1 and 6 is 1 (because every roll will give one of these numbers). Since it’s guaranteed, its probability is 1.
(iv) The sum of the probabilities of all the elementary events of an experiment is 1.
- Explanation:
In any experiment, the elementary events cover every possible outcome. For example, in a dice roll, the elementary events are rolling a 1, 2, 3, 4, 5, or 6. The total probability of all these events must be 1 because one of them is sure to happen. So, P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.
- Explanation:
Probabilities are always between 0 and 1. A probability of 0 means the event is impossible (it can’t happen), and a probability of 1 means the event is certain (it will happen). Probabilities cannot go below 0 or above 1.