Probability
Elementary event: Elementary
event is the event that has a single sample point. Like the occurrence of a
head when a coin is tossed.
Compound event: A compound event
happens when two or more elementary events happen at the same time. For
example: tossing of two coins.
Impossible event: Impossible
events are those whose have the probability of occurrence is zero. Like the occurrence of a 7 when a dice having
numbers from 1 to 6 is rolled.
Sure event: Sure event are those
whose occurrence is sure to happen. For example the event of getting a number
less than 7 when a dice having numbers 1 to 6 is rolled.
Equally likely event: Equally
likely events are those that can occur without any preferences to any one of
them. Example is the occurrence of a head or tail when a fair coin is tossed.
Favorable event: Favorable
events are those whose occurrence is favorable to the experiment we are doing. For
example let’s say the sample space of our experiment E is the occurrence of
even number when a dice is rolled. Then the occurrence of 2, 4, 6 are the
favorable events.
Complementary events :
Complementary events are those events that have not occurred when some event have
happened. Example is the rolling of dice. If the face of dice with a 2 has shown up then rest of the faces
1,3,4,5,6 are complementary.
Mutually exclusive event :
Mutually exclusive events are those when occurrence of one doesn’t mean the
occurrence of the other.
For example there are two events ,E1 occurrence of an even number
when a dice is rolled and E2 is the occurrence of a odd number when a dice is
rolled. If E1 has happened then E2 would not have occurred.
Important terms related to
probability
1.
วพ - it denotes the empty set. That means none of
the event has occured
2.
S is the sample space.
3.
E is the event
Then,
1.
P (¢) = 0 that is the probability of nothing happening is
zero. For example when a dice is rolled then the chances of not getting a
number is nil.
2.
P(S) = 1 that is the probability of occurring
the either of the number 1,2,3,4,5,6 when a dice is rolled is absolute.
3.
P(E) probability of occurrence of an event
lies 0≤P(E)≤1
Odds in favor and odds in against
When the chances of occurring of
an event are m and chances of an event not happening is n. Then,
The odds in favor = m: n
And the odds against the event =
n:
m
Theorems related to probability
are
1 .
If A and B are the only two events associated
with a random experiment then
P (A U B) = P (A) + P(B) – P(A∩B)
If the events A and B are mutually exclusive (have no occurrence in
common) then
P (A U B) = P (A) + P (B)
2.
If A , B and C are the only three events
associated with a random experiment then
P (A U B U C) = P (A) + P (B) +P(C)
– P (A∩B) – P (B∩C) – P (C∩A) + P (A∩B∩C)
If the events A, B and C are mutually exclusive (have no occurrence in
common) then
P (A U B U C) = P (A) + P (B) +P(C)
3.
If A and B are the two events and A ¢ B then
P(A) ≤P(B)
4.
For any events A and B
1. P (A -B) = P (A) – P (A∩B)
2.P (B -A) = P (B) – P (A∩B)
3.P (A` ∩ B) = P (B) – P (A∩B)
4.P (A ∩ B`) = P (A) – P (A∩B)
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