sample space for rolling two dice using tree diagram. Solution When we roll two dice, since each die contain faces marked with , , , , , the tree diagram will look like Hence, the sample space can be written as S= {( , ),( , ),( , ),( , ),( , ),( , ) ( , ),( , ),( , ),( , ),( , ),( , ) ( , ),( , ),( , ),( , ),( , ),( , ) ( , ),( , ),( , ),( , ),( , ),( , ) ( , ),( , ),( , ),( , ),( , ),( , ) ( , ),( , ),( , ),( , ),( , ),( , )} Fig. . Fig.
. H H H T T Fig. . T Event : In a random experiment, each possible outcome is called an event .
Thus, an event will be a subset of the sample space. Example : Getting two heads when we toss two coins is an event. Trial : Performing an experiment once is called a trial . Example : When we toss a coin thrice, then each toss of a coin is a trial.
Events Explanation Example Equally likely events Two or more events are said to be equally likely if each one of them has an equal chance of occurring. Head and tail are equally likely events in tossing a coin . Certain events In an experiment, the event which surely occur is called certain event . When we roll a die , the event of getting any natural number from one to six is a certain event.
Impossible events In an experiment if an event has no scope to occur then it is called an impossible event . When we toss two coins , the event of getting three heads is an impossible event. Mutually exclusive events Two or more events are said to be mutually exclusive if they don’t have common sample points. i.e., events A, B are said to be mutually exclusive if ∩ = f .
When we roll a die the events of getting odd numbers and even numbers are mutually exclusive events. Exhaustive events The collection of events whose union is the whole sample space are called exhaustive events . When we toss a coin twice , the collection of events of getting two heads, exactly one head, no head are exhaustive events. Complementary events The complement of an event