Mutually Exclusive Events
In general, it is true that for an event E:
P(
The event E , representing ‘not E’, is called the complement of the event E. We also say that E and
Before proceeding further, let us try to find the answers to the following questions:
(i) What is the probability of getting a number 8 in a single throw of a die?
To get number 8 in a single throw, we need to have a number 8 on the die which isn't possible. That is, the probability of an event which is impossible to occur is
Such an event is called an impossible event.
(ii) What is the probability of getting a number less than 7 in a single throw of a die?
Since every face of a die is marked with a number less than 7, it is sure that we will always get a number less than 7 when it is thrown once. So, the number of favourable outcomes is the same as the number of all possible outcomes, which is
Therefore, P(E) = P(getting a number less than 7) =
For an event, where the probability was 1(getting a number less than 7) it is known as an sure event or certain event.
Note : From the definition of the probability P(E), we see that the numerator (number of outcomes favourable to the event E) is always