. Probability Few centuries ago, gambling and gaming were considered to be fashionable and became widely popular among many men. As the games became more complicated, players were interested in knowing the chances of winning or losing a game from a given situation. In , Chevalier de Mere, a French nobleman with a taste of gambling, wrote a letter to one of the prominent mathematician of the time, Blaise Pascal, seeking his advice about how much dividend he would get for a gambling game played by paying money.
Pascal worked this problem mathematically but thought of sharing this problem and see how his good friend and mathematician Pierre de Fermat could solve. Their subsequent correspondences on the issue represented the birth of Probability Theory as a new branch of mathematics. Random Experiment A random experiment is an experiment in which (i) The set of all possible outcomes are known (ii)Exact outcome is not known. Blaise Pascal Statistics and Probability Example : .
Tossing a coin. . Rolling a die. Sample space The set of all possible outcomes in a random experiment is called a sample space .
It is generally denoted by S . Example : When we roll a die, the possible outcomes are the face numbers , , , , , of the die. Therefore the sample space is S = { , , , , , } Sample point Each element of a sample space is called a sample point . .
. Tree diagram Tree diagram allow us to see visually all possible outcomes of an random experiment. Each branch in a tree diagram represent a possible outcome. Illustration (i) When we throw a die, then from the tree diagram (Fig.
. ), the sample space can be written as S = { , , , , , } (ii) When we toss two coins, then from the tree diagram (Fig. . ), the sample space can be written as S={ HH,HT,TH,TT } Progress Check .
An experiment in which a particular outcome cannot be predicted is called . . The set of all possible outcomes is called . Example .