Suppose the events ${\mathbf{B}}_1$and ${\mathbf{B}}_2$are mutually exclusive and complementary events, such that$\mathbf{P}\mathbf{(}{\mathbf{B}}_1\mathbf{)}\mathbf{=}\mathbf{.}\mathbf{75}$and$\mathbf{P}\mathbf{(}{\mathbf{B}}_2\mathbf{)}\mathbf{=}\mathbf{.}\mathbf{25}$ Consider another event A such that role="math" localid="1658212959871" $\mathbf{P}\mathbf{\left(}\frac{\mathbf{A}}{{\mathbf{B}}_{\mathbf{1}}}\mathbf{\right)}\mathbf{=}\mathbf{.}\mathbf{3}$, role="math" localid="1658213029408" $\mathbf{P}\mathbf{\left(}\frac{\mathbf{A}}{{\mathbf{B}}_{\mathbf{2}}}\mathbf{\right)}\mathbf{=}\mathbf{.}\mathbf{5}$.

1. Find$\mathbf{P}\mathbf{(}{\mathbf{B}}_{\mathbf{1}}\mathbf{\cap }\mathbf{A}\mathbf{)}$.
2. Find$\mathbf{P}\mathbf{(}{\mathbf{B}}_2\cap \mathbf{A}\mathbf{)}$
3. Find P(A) using part a and b.
4. Findrole="math" localid="1658213127512" $\mathbf{P}\mathbf{\left(}\frac{{\mathbf{B}}_{\mathbf{1}}}{\mathbf{A}}\mathbf{\right)}$.
5. Findrole="math" localid="1658213164846" $\mathbf{P}\mathbf{\left(}\frac{{\mathbf{B}}_{\mathbf{2}}}{\mathbf{A}}\mathbf{\right)}$.

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