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PROBABILITY - 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)**

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