## Sample Space and Events

The **sample space** is the set of all possible outcomes in an experiment.

__Example 1:__ If a die is rolled, the sample space S is given by

S = {1,2,3,4,5,6}

__Example 2:__ If two coins are tossed, the sample space S is given by

S = {HH,HT,TH,TT} , where H = head and T = tail.

__Example 3:__ If two dice are rolled, the sample space S is given by

S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }

The event of interest is "getting a 3". so E = {3}.

The number of possible outcomes in E is 1 and the number of possible outcomes in S is 6. Hence the probability of getting a 3 is
P(E) = 1 / 6.

The event of interest is "getting an even number". so E = {2,4,6}, the even numbers on a die.

The number of possible outcomes in E is 3 and the number of possible outcomes in S is 6. Hence the probability of getting an even number is
P(E) = 3 / 6 = 1 / 2.

If a student is selected at random from this school, what is the probability that this student is in grade 3?

Let event E be "student from grade 3". Hence