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In each of the following experiments specify appropriate sample space A boy has a $1$ rupee coin, a $2$ rupee coin and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket, one after the other.
$S =\{ QH ,\, QR ,\, HQ , \,HR , \,RH ,\, RQ \}$
$S =\{ QH ,\, QR ,\, HQ , \,HR , \,RH ,\, RQ \}$
$S =\{ QH ,\, QR ,\, HQ , \,HR , \,RH ,\, RQ \}$
$S =\{ QH ,\, QR ,\, HQ , \,HR , \,RH ,\, RQ \}$
Solution
Let $Q$ denote a $1$ rupee coin, $H$ denotes a $2$ rupee coin and $R$ denotes a $5$ rupee coin. The first coin he takes out of his pocket may be any one of the three coins $Q$, $H$ or $R$. Corresponding to $Q$. the second draw may be $H$ or $R$. So the result of two draws may be $QH$ or $QR$. Similarly, corresponding to $H$, the second draw may be $Q$ or $R$.
Therefore, the outcomes may be $HQ$ or $HR$. Lastly, corresponding to $R$, the second draw may be $H$ or $Q$.
So, the outcomes may be $RH$ or $RQ$.
Thus, the sample space is $S =\{ QH ,\, QR ,\, HQ , \,HR , \,RH ,\, RQ \}$
