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Question

A coin is tossed repeatedly until a tail comes tip for the first time. Write the sample space for this experiment.


Solution

In this experiment, a coin is tossed and if the outcome is tail the experiment is over.

Otherwise, the coin is tossed again. 

In the second toss also if the outcome is tail the experiment is over, otherwise tossed again. 

In the third toss, if the outcome is tail, the experiment is over, otherwise tossed again. 

This process continues indefinitely. 

Hence, the sample space S associated to this random experiment is 

S = {T, HT, HHT, HHHT, HHHHT, ....} 

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