Given: Total number of watches =
![\[100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a40261fc9a48539be6f3f3cac1241623_l3.png "Rendered by QuickLaTeX.com")
and number of defective watches =
![\[10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e13914576c8f07fa7780b4b1aae684d_l3.png "Rendered by QuickLaTeX.com")
So, the probability of selecting a detective watch =
![\[10/100\text{ }=\text{ }1/10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8e1eb4a081f46661dc66b12e57aedf0e_l3.png "Rendered by QuickLaTeX.com")
Now,
n =
![\[8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ba6e07885b354f6c76c81fbd23c392a_l3.png "Rendered by QuickLaTeX.com")
,
![\[p\text{ }=\text{ }1/10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7006cf113af85c1e6197f4dae3842594_l3.png "Rendered by QuickLaTeX.com")
and
![\[q\text{ }=\text{ }1\text{ }\text{ }1/10\text{ }=\text{ }9/10,\text{ }r\text{ }\ge \text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a865018f02916aaf6367a9a216210db7_l3.png "Rendered by QuickLaTeX.com")
![\[P\left( X\text{ }\ge \text{ }1 \right)\text{ }=\text{ }1\text{ }\text{ }P\left( x\text{ }=\text{ }0 \right)\text{ }=\text{ }1\text{ }{{~}^{8}}{{C}_{0}}~{{\left( 1/10 \right)}^{0}}{{\left( 9/10 \right)}^{8\text{ }\text{ }0}}~=\text{ }1\text{ }\text{ }{{\left( 9/10 \right)}^{8}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-fdddebc1c96c6f441ec72635c0760466_l3.png "Rendered by QuickLaTeX.com")
Therefore, the required probability is
![\[1\text{ }\text{ }{{\left( 9/10 \right)}^{8}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-031e13f6a20a447d704ab76a71404269_l3.png "Rendered by QuickLaTeX.com")
.
A lot of
Given: Total number of watches =
and number of defective watches =
So, the probability of selecting a detective watch =
Now,
n =
,
and
Therefore, the required probability is
.