A Note The outcomes of this experiment are ordered pairs of H and T. For the sake of simplicity the commas are omitted from the ordered pairs. Example Find the sample space associated with the experiment of rolling a pair of dice (one is blue and the other red) once. Also, find the number of elements of this sample space.
Solution Suppose appears on blue die and on the red die. We denote this outcome by an ordered pair ( , ). Similarly, if ‘ ’ appears on blue die and ‘ ’ on red, the outcome is denoted by the ordered pair ( , ). In general each outcome can be denoted by the ordered pair ( x , y ), where x is the number appeared on the blue die and y is the number appeared on the red die.
Therefore, this sample space is given by S = {( x , y ): x is the number on the blue die and y is the number on the red die}. The number of elements of this sample space is × = and the sample space is given below: {( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ) ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ) ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , )} Example In each of the following experiments specify appropriate sample space A boy has a rupee coin, a rupee coin and a rupee coin in his pocket. He takes out two coins out of his pocket, one after the other. A person is noting down the number of accidents along a busy highway during a year.
Solution (i) Let Q denote a rupee coin, H denotes a rupee coin and R denotes a rupee coin. The first coin he takes out of his pocket may be any one of the three coins Q, H or R. Corresponding to Q, the second draw may be H or R. So the result of two draws may be QH