I believe if you keep your faith, you keep your trust, you keep the right attitude, if you’re grateful, you’ll see God open up new doors. ..

In this Chapter, we studied about the axiomatic approach of probability.
The main features of this Chapter are as follows:

Sample space: The set of all possible outcomes
Sample points: Elements of sample space
Event: A subset of the sample space
Impossible event : The empty set
Sure event: The whole sample space

Complementary event or ‘not event’ : The set A′ or S – A 

Event A or B: The set A ∪ B
Event A and B: The set A ∩ B
Event A and not B: The set A – B
Mutually exclusive event: A and B are mutually exclusive if A ∩ B = φ
Equally likely outcomes: All outcomes with equal probability
Probability of an event: For a finite sample space with equally likely outcomes
Probability of an event \( P(A) = \frac{n(A)}{n(S)} \), where n(A) = number of elements in the set A,
n(S) = number of elements in the set S.
If A and B are any two events, then
P(A or B) = P(A) + P(B) – P(A and B) equivalently,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
If A and B are mutually exclusive, then P(A or B) = P(A) + P(B)
If A is any event, then
P(not A) = 1 – P(A)

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