die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment. .
A coin is tossed. If it shows a tail, we draw a ball from a box which contains red and black balls. If it shows head, we throw a die. Find the sample space for this experiment.
. A die is thrown repeatedly untill a six comes up. What is the sample space for this experiment? .
Event We have studied about random experiment and sample space associated with an experiment. The sample space serves as an universal set for all questions concerned with the experiment. Consider the experiment of tossing a coin two times. An associated sample space is S = {HH, HT, TH, TT}.
Now suppose that we are interested in those outcomes which correspond to the occurrence of exactly one head. We find that HT and TH are the only elements of S corresponding to the occurrence of this happening (event). These two elements form the set E = { HT, TH} We know that the set E is a subset of the sample space S . Similarly, we find the following correspondence between events and subsets of S.
MATHEMATICS Description of events Corresponding subset of ‘S’ Number of tails is exactly A = {TT} Number of tails is atleast one B = {HT, TH, TT} Number of heads is atmost one C = {HT, TH, TT} Second toss is not head D = { HT, TT} Number of tails is atmost two S = {HH, HT, TH, TT} Number of tails is more than two φ The above discussion suggests that a subset of sample space is associated with an event and an event is associated with a subset of sample space. In the light of this we define an event as follows. Definition Any subset E of a sample space S is called an event . .
. Occurrence of an event Consider the experiment of