# CLASS-10PROBABILITY - SOME IMPORTANT EVENTS

SOME IMPORTANT EVENTS OF PROBABILITY -

There are some important and useful events of probability has been discussed below

Sure Event

Suppose we throw a die. Clearly, the upper face of it will always show a number less than 7.

So, getting a number less than 7 is a sure event.

P (getting a number less than 7) = 6/6 = 1

Thus, the probability of a sure event is 1.

Impossible Event

In a single toss of a die, what is the probability of getting the number 7 ?

Clearly, in tossing a die, 7 will never come up.

So, getting 7 is impossible event.

0

So, P(getting 7 in a single throw of a die) = --------  = 0

6

Hence, the probability of an impossible event is 0 (Zero).

Complementary Event

Let, E be an event and (not E) be an event which occurs only when E does not occur.

The event (not E) is called the complementary event of E

Clearly, P(E) + P(not E) = 1

P(E) = 1 – P(not E)

Summery

(i) For any event E, we have 0 < P(E) < 1

(ii)  If E is an impossible event, then P(E) = 0

(iii) If E is a sure event, we have P(E) = 1

(iv) P(not E) = 1 – P(E)