An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

Let H denote the event of a head and T denote the event of a tail,

1,2,3,4,5,6 denote the event the respective numbers come when the die is thrown

The problem can be solved by breaking it into two cases

Case 1: Head is encountered

We define the possible outcomes by an ordered set (x, y)

x denotes the first event when the head is encountered

y denotes the second event the coin is tossed again

Sample space S₁={(H,T),(H,H)}

Case 2: Tail is encountered

We define the possible outcomes by an ordered set (x, y)

x denotes the first event when the tail is encountered

y denotes the second event when the die is thrown

Sample Space S₂={(T,1),(T,2),(T,3),(T,4),(T,5),(T,6)}

The Overall Sample space

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