![\[\mathbf{1}\text{ }\mathbf{to}\text{ }\mathbf{100}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-656d6106f414a60095504a0e75cdbb9a_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{i} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ec4588e8cb8288d41d93726c3b60fee0_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a776c358a8cf31774e7e50698744b5e6_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{ii} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a4cc96f58fba9e185f598e5aebb7decb_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{6}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-263adac88912153e6b4347f4b5c18c13_l3.png "Rendered by QuickLaTeX.com")
Solution:
We kwon that, there are
![\[100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a40261fc9a48539be6f3f3cac1241623_l3.png "Rendered by QuickLaTeX.com")
cards from which one card is drawn.
Total number of elementary events
![\[=\text{ }n\left( S \right)\text{ }=\text{ }100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cde217bb53d79ba62997614501fefff4_l3.png "Rendered by QuickLaTeX.com")
![\[\left( i \right)~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-48b1ef2e28a71618f5ba50733f552ee1_l3.png "Rendered by QuickLaTeX.com")
From numbers
![\[1\text{ }to\text{ }100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-36c33572fcc0e7e6b271203f980da6f7_l3.png "Rendered by QuickLaTeX.com")
there are
![\[20\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f909910e2f598933c23989d90a7a4169_l3.png "Rendered by QuickLaTeX.com")
numbers which are multiple of 5 i.e.
![\[\{5,\text{ }10,\text{ }15,\text{ }20,\text{ }25,\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c0af3c2351304c532c95523bc0bdc12_l3.png "Rendered by QuickLaTeX.com")
![\[30,\text{ }35,\text{ }40,\text{ }45,\text{ }50,\text{ }55,\text{ }60,\text{ }65,\text{ }70,\text{ }75,\text{ }80,\text{ }85,\text{ }90,\text{ }95,\text{ }100\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4b26f5946af354d16c6b194bdeae7aa1_l3.png "Rendered by QuickLaTeX.com")
So, favorable number of events
![\[=\text{ }n\left( E \right)\text{ }=\text{ }20\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-53a398f543e2d85d294c108104f46b82_l3.png "Rendered by QuickLaTeX.com")
Hence, probability of selecting a card with a multiple of
![\[5\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }20/\text{ }100\text{ }=\text{ }1/5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-56f72824b9902415a7f5628b1173b02e_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
![\[16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a9afcd935e0b07e58e19bb7c3d7d4534_l3.png "Rendered by QuickLaTeX.com")
numbers which are multiple of
![\[6\text{ }i.e.~\{6,\text{ }12,\text{ }18,\text{ }24\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6105bd941b9ed4005a0455f8b52563c9_l3.png "Rendered by QuickLaTeX.com")
,
![\[30,\text{ }36,\text{ }42,\text{ }48,\text{ }54,\text{ }60,\text{ }66,\text{ }72,\text{ }78,\text{ }84,\text{ }90,\text{ }96\}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-29bf243f920f9270699709c175e72105_l3.png "Rendered by QuickLaTeX.com")
So, favorable number of events
![\[=\text{ }n\left( E \right)\text{ }=\text{ }16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-307f11f9ad37ced41420b60b1fe1c92b_l3.png "Rendered by QuickLaTeX.com")
Hence, probability of selecting a card with a multiple of
![\[6\text{ }=\text{ }n\left( E \right)/\text{ }n\left( S \right)\text{ }=\text{ }16/\text{ }100\text{ }=\text{ }4/25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dee4293d10b3adc274f585db86a04603_l3.png "Rendered by QuickLaTeX.com")
