Q. 123.9( 20 Votes )

A coin is t

Answer :

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 come when the die is thrown


The problem can be solved by dividing it into 3 cases


Case 1: Head is encountered and the corresponding number on the die is Odd


Total number of sample space=(1×3)=3


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


x denotes the first event the head is encountered


y denotes the second event the number on the die is Odd


Sample space S1={(H,1),(H,3),(H,5)}


Case 2: Head is encountered and the corresponding number is even


Total number of sample space=(1×3×6)=18


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


where


x denotes the outcomes when the coin is tossed and head is encountered


y denotes the outcomes when the die is tossed and the number encountered is even


z denotes the outcomes when the die is tossed for the second time


Sample Space


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


Case 3: Tail is encountered


Total number of sample space=1


Sample space S3={(T)}


The overall sample spaces


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


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