1.

A balanced coin in thrown in a random experiment till the first head is obtained. The experiment is terminated with a trial of first head. Write the sample space of this experiment and state whether it is finite or infinite.

Answer»

A balanced coin is thrown till the first head is obtained.

The options of this random experiment are as follows :

  • Head (H) is obtained in the first trial, i.e., outcome H is obtained.
  • Tail (T) is obtained in the first trial and Head (H) is obtained in second trial, i.e., outcome TH is obtained.
  • Tail (T) is obtained in first two trials and Head (H) is obtained in third trial, i.e., outcome TTH is obtained.
  • Tail (T) is obtained in first three trials and Head (H) is obtained in fourth trial, i.e., outcome TTTH is obtained.

In this manner outcomes TTTTH, TTTTTH, … are obtained. Thus, the number of outcomes of this random experiment is indefinite.

Hence, the sample space of the random experiment of throwing a balanced coin till the first head is obtained, is expressed as follows:

U = (H, TH, TTH, TTTH, …}

The sample space of this experiment is infinite.


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