Chapter 7.6, Problem 10E

The accompanying tree diagram represent a two stage experiment. Use the diagram to find:

a. $P\left(A\cap D\right)$

b. $P\left(B\cap D\right)$

c $P\left(C\cap D\right)$

d $P\left(D\right)$

e. Verify:

$\begin{array}{rll}P\left(A|D\right)& =& \frac{P\left(A\cap D\right)}{P\left(D\right)}\\ & =& \frac{P\left(A\right)\cdot P\left(D|A\right)}{P\left(A\right)\cdot P\left(D|A\right)+P\left(B\right)\cdot P\left(D|B\right)+P\left(C\right)\cdot P\left(D|C\right)}\end{array}$