Find the indicated probability by using the general addition rule.
-Let $\mathrm { A }$ and $\mathrm { B }$ be events such that $\mathrm { P } ( \mathrm { A } ) = \frac { 1 } { 7 } , \mathrm { P } ( \mathrm { A }$ or $\mathrm { B } ) = \frac { 1 } { 6 }$, and $\mathrm { P } ( \mathrm { A }$ and $\mathrm { B } ) = \frac { 1 } { 12 }$. Determine $\mathrm { P } ( \mathrm { B } )$.
A)$\frac { 5 } { 84 }$
B) $\frac { 3 } { 28 }$
C) $\frac { 1 } { 42 }$
D) $\frac { 11 } { 28 }$

Question

Find the indicated probability by using the general addition rule.
-Let $\mathrm { A }$ and $\mathrm { B }$ be events such that $\mathrm { P } ( \mathrm { A } ) = \frac { 1 } { 7 } , \mathrm { P } ( \mathrm { A }$ or $\mathrm { B } ) = \frac { 1 } { 6 }$, and $\mathrm { P } ( \mathrm { A }$ and $\mathrm { B } ) = \frac { 1 } { 12 }$. Determine $\mathrm { P } ( \mathrm { B } )$.  
A)$\frac { 5 } { 84 }$
B) $\frac { 3 } { 28 }$
C) $\frac { 1 } { 42 }$
D) $\frac { 11 } { 28 }$

Quizplus · Accepted Answer

Using the general addition rule: $ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) $. Plugging in the values: $\frac{1}{6} = \frac{1}{7} + P(B) - \frac{1}{12}$. Solving for $ P(B) $ gives $\frac{3}{28}$.

Find the Indicated Probability by Using the General Addition Rule A\mathrm { A }A

Find the Indicated Probability by Using the General Addition Rule $\mathrm { A }$