$A$ die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
In this experiment,the die is thrown until a $6$ appears. Let $S$ denote the sample space.
If $6$ appears on the first throw,the outcome is $6$.
If $6$ appears on the second throw,the outcome is $(x, 6)$ where $x \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the third throw,the outcome is $(x, y, 6)$ where $x, y \in \{1, 2, 3, 4, 5\}$.
Continuing this process,the sample space $S$ is given by:
$S = \{6, (x, 6), (x, y, 6), (x, y, z, 6), \dots \}$ where $x, y, z, \dots \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the first throw,the outcome is $6$.
If $6$ appears on the second throw,the outcome is $(x, 6)$ where $x \in \{1, 2, 3, 4, 5\}$.
If $6$ appears on the third throw,the outcome is $(x, y, 6)$ where $x, y \in \{1, 2, 3, 4, 5\}$.
Continuing this process,the sample space $S$ is given by:
$S = \{6, (x, 6), (x, y, 6), (x, y, z, 6), \dots \}$ where $x, y, z, \dots \in \{1, 2, 3, 4, 5\}$.
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DifficultTS EAMCET 2003
View Solution$A$ fair die is tossed twice in succession. If $X$ denotes the number of sixes in $2$ tosses,then the probability distribution of $X$ is given by
Consider the probability distribution
$\begin{array}{|r|c|c|c|c|c|} \hline X=x & 1 & 2 & 3 & 4 & 5 \\ \hline P(X=x) & K & 2K & K^2 & 2K & 5K^2 \\ \hline \end{array}$
Then the value of $P(X > 2)$ is
$\begin{array}{|r|c|c|c|c|c|} \hline X=x & 1 & 2 & 3 & 4 & 5 \\ \hline P(X=x) & K & 2K & K^2 & 2K & 5K^2 \\ \hline \end{array}$
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