Question

Complete the following statements:

1. Probability of an event E + Probability of the event not E = __________.
2. The probability of an event that cannot happen is . Such an event is called___.
3. The probability of an event that is certain to happen is . Such an event is called___.
4. The sum of the probabilities of all the elementary events of an experiment is ________.
5. The probability of an event is greater than or equal to _______ and less than or equal to ________.

Answer 1

Hint: As we know that probability means possibility. It deals with the occurrence of random events. Mathematically it lies between 0 and 1. Where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space sums up to 1.
An event which always happens is called a sure event. An event that cannot happen is known as an impossible event.
Probability of event to happen P(E) $=\dfrac{\text{Number of favourable outcomes}}{\text{Total Number of outcomes}}$

Complete step-by-step answer:
For question 1:
Let us assume an event E whose probability is P(E).
As we know that probability of all the events in a sample space = 1
Therefore, Probability of an event not E = 1- Probability of an event E
Probability of an event E + Probability of an event not E = 1
For question 2:
We also know that an event that cannot happen has probability 0.
An event that cannot happen is called an impossible event.
For question 3:
The event that is certain to happen means that only this event has occurred.
Therefore, the probability of an event that is certain to happen is 1. And such an event is called a sure event.
For question 4:
Sum of the probabilities of all the elementary events of an experiment means that all the events in a sample space.
Therefore, The sum of the probabilities of all the elementary events of an experiment is 1.
For question 5:
As we know that the probability of any event lies between 0 and 1. Therefore, its minimum value is 0 and maximum value is 1.
Hence, The probability of an event is greater than or equal to 0 and the probability of an event less than or equal to 1.

Note: While solving such questions, we should have the basic knowledge of probability. We must remember its range is from 0 to 1. Don’t get confused with sure events and impossible events. Probability of sure event is 1 and probability of impossible event is 0.