A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Let H denote the event of a head and T denote the event of a tail when coin is tossed

R₁, R₂ denote the event the red balls are drawn B₁, B₂, B₃ denote the events black ball are drawn

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

The following problem can be divided in two cases

Case 1: Tail turns up in the coin

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

x denotes the first event the coin is tossed and tails turns up

y denotes the second event a ball is drawn

The sample space S₁={(T,R₁),(T,R₂),(T,B₁),(T,B₂),(T,B₃)}

Case 2: Head turns up in the coin

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

x denotes the first event the coin is tossed and head turns up

y denotes the second event the die is thrown

The sample space S₂={(H,1),(H,2),(H,3),(H,4),(H,5),(H,6)}

Therefore, the overall sample space for the problem= S₁+ S₂

S={( T,R₁),(T,R₂),(T,B₁),(T,B₂),(T,B₃),(H,1),(H,2),(H,3),(H,4),(H,5),(H,6)}