A die is thrown once. Find the probability of getting (i) a number lying between 2 and 6; (ii) an odd number.

Step 1: Identify the sample space and number of possible outcomes
NOTE: The sample space of an experiment or random trial is the set of all
possible outcomes or results of that experiment
Die has sample space S = {1, 2, 3, 4, 5, 6}
Number of outcomes n(S) = 6
Step 2: Find the favorable outcomes of the event.
(i) list out the numbers lying between 2 and 6
= {3, 4, 5}
So, Favourable outcomes = 3
(ii) List out the odd numbers = {1, 3, 5}
So, Favourable out comes = 3
Step 2: Calculate the probability
Probability of getting a number lying between 2 and 6 = \frac{3}{6} = \frac{1}{2}
Probability of getting a number an odd number = \frac{3}{6} = \frac{1}{2}