According to the question:
Bag
![\[1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-64318110f3a374fb786ef713c0b0c575_l3.png "Rendered by QuickLaTeX.com")
has
![\[3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-df8bcc09db12acd0f6bda88b4b8135fb_l3.png "Rendered by QuickLaTeX.com")
B,
![\[2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b1e8e3db630df9050b1fec3c4066d5e6_l3.png "Rendered by QuickLaTeX.com")
W balls and Bag
has
B,
![\[4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c0fa656ae249b0b1e03c8cd2e7be583_l3.png "Rendered by QuickLaTeX.com")
W balls.
Let
![\[{{E}_{1}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a18b4f4210098684c3183f0c3d29ae73_l3.png "Rendered by QuickLaTeX.com")
= The event that bag
is selected
![\[{{E}_{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0730822ca38b76c410dc8658f334d0de_l3.png "Rendered by QuickLaTeX.com")
= The event that bag
is selected
And, E = The event that a black ball is selected
Now, the probabilities are:
Therefore, the required probability is
![\[7/15\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1009b8b3ea8ea5a12eb54fca4baadd79_l3.png "Rendered by QuickLaTeX.com")
.