Corrected Chapter 2, 43b.

Author: Paciic

src/chapters/2/sections/monty_hall/problems/43.tex

@@ -25,10 +25,11 @@
 &= \frac{P(C_{3})P(D_{2}, O_{2} | C_{3})}{P(C_{3})P(D_{2}, O_{2} | C_{3}) + P(C_
 {3}^{c})P(D_{2}, O_{2} | C_{3}^{c})} \\
 &= \frac{\frac{1}{3}P(O_{2}|C_{3})P(D_{2}|O_{2}, C_{3})}{\frac{1}{3}P(O_{2}|C_
-{3})P(D_{2}|O_{2}, C_{3}) + P(C{3}^{c})P(D_{2}, O_{2} | C_{3}^{c})} \\
+{3})P(D_{2}|O_{2}, C_{3}) + P(C_{3}^{c})P(D_{2}, O_{2} | C_{3}^{c})} \\
 &= \frac{\frac{1}{3}*\frac{1}{2}*p}{\frac{1}{3}*\frac{1}{2}*p + \frac{2}
 {3}*\frac{1}{4}*q} \\
 &= \frac{\frac{1}{6}p}{\frac{1}{6}p + \frac{1}{6}q} \\
-&= \frac{1}{2}p.
+&= \frac{p}{p+(1-p)} \\
+&= p.
 \end{align*}
-\end{enumerate}
+\end{enumerate}