Question 1028576
Two express delivery companies A and B advertise that they 
will deliver a package anywhere in Namibia within 24 hours.
Company A delivers 70% of such packages and company B the 
rest.  It is known that 5 % of the packages delivered by 
Company A are late, and 2% of those delivered by Company B 
are late.
<pre><b>
1.Present this information on a tree diagram.

{{{drawing(600,300,-1,15,-5,5,

line(0,0,3.5,1.75), line(4.5,2.25,6,3),

 line(4.5,1.75,6,1),

line(0,0,3.5,-1.75),
 line(4.5,-2.25,6,-3),

 line(4.5,-1.75,6,-1),




locate(1.8,1.75,0.7), locate(1.8,-.29,0.3),locate(3.95,2.3,A),

locate(3.95,-1.7,B), locate(4.7,3.3,0.95),

locate(4.7,2,0.05),

locate(4.7,3.3-4,0.98),

locate(4.7,2-4,0.02)  
  
locate(6,3.4,matrix(1,3,on,"time,",probability=(0.7)(0.95)=0.665)),
locate(6.1,1.4,matrix(1,2,"late,",probability=(0.7)(0.05)=0.035)),
locate(6.1,-.6,matrix(1,3,on,"time,",probability=(0.3)(0.98)=0.294)),
locate(6.1,-2.6,matrix(1,2,"late,",probability=(0.3)(0.02)=0.006))


)}}} 
</pre>
2. If a package is selected from the shipment at random what 
is the probability that package will be delivered late?
<pre>
P(late) = 0.035+0.006 = 0.041
</pre>
3.What is the probability that a package that was received 
late was delivered by Company B?
<pre>
That asks for the probability that it was delivered by 
Company B given that it was late.

{{{"P(B|late)" = P(matrix(1,3,B,and,late))/"P(late)"=.006/0.041=6/41}}}

Edwin</pre></b>