# An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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

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

The following problem can be divided in two cases

Case 1: Even number shows up in the die

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

x denotes the first event even number shows up

y denotes the second event a coin is thrown

The sample space S1={(2,H),(4,H),(6,H),(2,T),(4,T),(6,T)}

Case 2: Odd number shows up in the die

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

x denotes the first event odd number shows up in the die

y denotes the second event the coin is thrown for first time

z denote the third event the coin is thrown for second time

The sample space

S2={(1,H,H),(3,H,H),(5,H,H),(1,H,T),(3,H,T),(5,H,T),(1,T,H),(3,T,H),(5,T,H),(1,T,T),(3,T,T),(5,T,T)}

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

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

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