Mutually exclusive events
Events A and B are called mutually exclusive events if occurrence of any one of them excludes occurrence of other event, i. e., if they cannot occur simultaneously.
Example: A die is thrown. Event A = All even outcome & event B = All odd outcome. Then A & B are mutually exclusive events, they cannot occur simultaneously.
Exhaustive events
Lot of events that together forms sample space. Example: A die is thrown. Event A = All even outcome & event B = All odd outcome. Even A & B together forms exhaustive events as it forms Sample Space.
Axiomatic Approach to Probability It is another way of describing probability. Here Axioms or rules are used.
Let S be sample space of a random experiment containing outcomes ω1, ω2,..., ωn, then
o P( ωi) ≥ 0 & P( S) = 1 è 0 ≤ P( ωi) ≤ 1 o P( ω1) + P( ω2) +... + P( ωn) = 1
o
For any event E, P( E) = Σ P( ωi), ωi ∈ o P( φ) = 0
Example: In a throw of two rigged coins, P( HH) = 1 / 4, P( HT) = 1 / 7, P( TH) = 2 / 7, P( TT) = 9 / 28. Find P( E) where E = Either both head or both Tail, E = One head, one Tail, E = Both tail
Solution:
P( E) where E = Either both head or both Tail. Since both these events are mutually exclusive events