Probability Formulas

                

1. Experiment

 An operation which can produce well-defined outcomes is called an experiment.

2. Random Experiment

If all the possible outcomes of an experiment are known but the exact output cannot be predicted in advance, that experiment is called a random experiment.

Examples

1. Tossing a fair coin
   When we toss a coin, the outcome will be either Head (H) or Tail (T)
2. Throwing an unbiased die
   Die is a small cube used in games. It has six faces and each of the six faces shows a different number of dots from 1 to 6. Plural of die is dice.
   When a die is thrown or rolled, the outcome is the number that appears on its upper face and it is a random integer from one to six, each value being equally like.
3. Drawing a card from a pack of shuffled cards
   A pack or deck of playing cards has 52 cards which are divided into four categories as given below
   1. Spades 
   2. Clubs 
   3. Hearts 
   4. Diamonds 
   Each of the above mentioned categories has 13 cards, 9 cards numbered from 2 to 10, an Ace, a King, a Queen and a jack
   Hearts and Diamonds are red faced cards whereas Spades and Clubs are black faced cards.
   Kings, Queens and Jacks are called face cards.

3. Sample Space

      When we perform an experiment,then the set of all possible outcome is called Sample space.      >It is denoted by 'S'.

Examples

1. When a coin is tossed, S = {H, T} where H = Head and T = Tail
2. When a dice is thrown, S = {1, 2 , 3, 4, 5, 6}
3. When two coins are tossed, S = {HH, HT, TH, TT} 

4. Probability Of Event

Let E be an event and S be the sample space. Then probability of the event E can be defined as

P(E) = n(E)n(S)

where P(E) = Probability of the event E, n(E) = number of ways in which the event can occur and n(S) = Total number of outcomes possible.

5. Results On Probability

i.  P(S)=1

ii. 0<_P(E)<

_1

iii. P(A U B) = P(A) + P(B) – P(A ∩

B)

iv. P(A¯)

= 1 - P(A)