Q. 144.2( 20 Votes )

An experime

Answer :

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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