What is Mutually Exlusive Event & Exhaustive Events ? Explain with example.
Let E1,E2....En be subsets of the sample space 'S' then, E1,E2.........En are said to be mutually exclusive and exhaustive if:
1) Ei intersection Ej = 0 or Phi (Ei and Ej are two Separate Events)
2) E1UE2U..........UEn = S
Example:
Consider a pack of 52 cards
Let E1,E2,E3,E4 be the event of drawing a club, a spade, a diamond and a heart
If the intersection of any two events are taken , we see that there is nothing in common and hence condition 1) is satisfied
Taking E1UE2UE3UE4 we get the whole deck of cards which is the Sample space and condition 2) is satisfied
Therefore E1,E2,E3,E4 are Mutually Exclusive and Exhaustive Events
1) Ei intersection Ej = 0 or Phi (Ei and Ej are two Separate Events)
2) E1UE2U..........UEn = S
Example:
Consider a pack of 52 cards
Let E1,E2,E3,E4 be the event of drawing a club, a spade, a diamond and a heart
If the intersection of any two events are taken , we see that there is nothing in common and hence condition 1) is satisfied
Taking E1UE2UE3UE4 we get the whole deck of cards which is the Sample space and condition 2) is satisfied
Therefore E1,E2,E3,E4 are Mutually Exclusive and Exhaustive Events