![\[\mathbf{25}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-04c165886b06185d393c73aef1d22b23_l3.png "Rendered by QuickLaTeX.com")
![\[\text{ }\mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4},\text{ }\mathbf{5},\text{ }\ldots \ldots ,~\mathbf{24},\text{ }\mathbf{25}:\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1f2c87afd2f10bf14f5329adbf782f73_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{i} \right)\text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d29dcd8869a616f0d150912528867b07_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{ii} \right)\text{ }\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-196cc0b4d2efdb4a16e4b1ad1ff50340_l3.png "Rendered by QuickLaTeX.com")
Solution:
We know that, there are
![\[25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a1797b1bfd351a37de7d6fef1e296af4_l3.png "Rendered by QuickLaTeX.com")
cards from which one card is drawn.
So, the total number of elementary events
![\[=\text{ }n\left( S \right)\text{ }=\text{ }25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5a8d484390d3d0358b2d0914e74211c_l3.png "Rendered by QuickLaTeX.com")
![\[\left( i \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c013687aa5dbc1ecafb4bc91b7e8e7fe_l3.png "Rendered by QuickLaTeX.com")
From numbers
![\[1\text{ }to\text{ }25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a2ca170505202446250d2941a7202d76_l3.png "Rendered by QuickLaTeX.com")
, there are
![\[8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ba6e07885b354f6c76c81fbd23c392a_l3.png "Rendered by QuickLaTeX.com")
numbers which are multiple of
![\[3\text{ }i.e.~\{3,\text{ }6,\text{ }9,\text{ }12,\text{ }15,\text{ }18\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ee5e28b24e6ae084580663832f1ed226_l3.png "Rendered by QuickLaTeX.com")
,
![\[~21,\text{ }24\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e724da4bc56e6ef74a054e12ca543b14_l3.png "Rendered by QuickLaTeX.com")
So, favorable number of events
![\[=\text{ }n\left( E \right)\text{ }=\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-479be3a196f6cd6b5f2da2220ac7cf2c_l3.png "Rendered by QuickLaTeX.com")
Hence, probability of selecting a card with a multiple of
![\[3\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }8/25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3022c1d2152176f40d87f61c81e6483a_l3.png "Rendered by QuickLaTeX.com")
![\[\left( ii \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fb274751d677ea2ebc95af4c2f5fd659_l3.png "Rendered by QuickLaTeX.com")
From numbers
, there are
![\[5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7dc8465919d0838925dbc6c99670258c_l3.png "Rendered by QuickLaTeX.com")
numbers which are multiple of
![\[5\text{ }i.e.~\left\{ 5,\text{ }10,\text{ }15,\text{ }20,\text{ }25 \right\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e07321440929a6ae51dc9347b155ff40_l3.png "Rendered by QuickLaTeX.com")
So, favorable number of events
![\[=\text{ }n\left( E \right)\text{ }=\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7d24fb87b723ccfd6f91254915fb1fe6_l3.png "Rendered by QuickLaTeX.com")
Hence, probability of selecting a card with a multiple of
![\[5\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }5/25\text{ }=\text{ }1/5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-936de8e7ac35abb0f2981049cbfeb72f_l3.png "Rendered by QuickLaTeX.com")