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