Suppose the events ${\mathbf{B}}_1\mathbf{,}{\mathbf{B}}_2\mathbf{,}{\mathbf{B}}_3$ are mutually exclusive and complementary events, such that$\mathbf{P}\mathbf{(}{\mathbf{B}}_1\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}$, $\mathbf{P}\mathbf{(}{\mathbf{B}}_2\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{4}$and $\mathbf{P}\mathbf{(}{\mathbf{B}}_3\mathbf{)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{5}$. Consider another event A such that$\mathbf{P}\mathbf{\left(}\frac{\mathbf{A}}{{\mathbf{B}}_{\mathbf{1}}}\mathbf{\right)}\mathbf{=}\mathbf{P}\mathbf{\left(}\frac{\mathbf{A}}{{\mathbf{B}}_{\mathbf{2}}}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1}$and$\mathbf{P}\mathbf{\left(}\frac{\mathbf{A}}{{\mathbf{B}}_{\mathbf{3}}}\mathbf{\right)}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2}$Use Baye’s Rule to find

a.$\mathbf{P}\mathbf{\left(}\frac{{\mathbf{B}}_{\mathbf{1}}}{\mathbf{A}}\mathbf{\right)}$

b.$\mathbf{P}\left(\frac{{\mathbf{B}}_2}{A}\right)$

c.role="math" localid="1658214716845" $\mathbf{P}\mathbf{\left(}\frac{{\mathbf{B}}_{\mathbf{3}}}{\mathbf{A}}\mathbf{\right)}$

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