In each of the following, describe the sample space for the indicated experiment.

A coin is tossed and then a die is rolled only in case a head is shown on the coin.

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 comes 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 when the die is thrown

Sample Space S₁={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6)}

Case 2: Tail is encountered

Sample Space S₂={(T)}

The overall sample space S={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6),(T)}