Describe the sample space for the indicated experiment : A die is thrown two times.
Describe the sample space for the indicated experiment : A die is thrown two times.
When a die is thrown, the possible outcomes are $1,\,2,\,3,\,4,\,5,$ or $6$.
When a die is thrown two times, the sample is given by $S =\{(x, y): x , y =1,2,3,4,5,6\}$
The number of elements in this sample space is $6 \times 6=36,$ while the sample space is given by :
$S=\{(1,1),\,(1,2),\,(1,3)$, $( 1,4),\,(1,6),\,(2,1)$, $(2,2),\,(2,3),\,(2,4)$, $(2,5),\,(2,6),\,(3,1),$ $(3,2),\,(3,3),\,(3,4)$, $(3,5),$ $(3,6),\,(4,1)\,,(4,2)$, $(4,3),\,(4,4),\,(4,5),\,(4,6)$, $(5,1)\,,(5,2),$ $(5,3)\,,(5,4)\,,(5,5)$, $(5,6),\,(6,1),\,(6,2)$, $(6,3)$, $(6,4),\,(6,5),\,(6,6)\}$
Similar Questions
$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P ( A \cup B )$.
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$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$ $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$ $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$ $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$
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- [IIT 2017]
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