# An experime

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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