Question

A Peruvian human sacrificial temple, near Lima, Peru, has three
levels, levels J, M, and H, where tourists have the only access to
the temple.
The probabilities that a tourist visiting the temple will visit the
different levels are:
Visit level J: 0.74
Visit level M: 0.70
Visit level H: 0.62
Visit levels J and M: 0.52
Visit levels J and H: 0.46
Visit levels M and H: 0.44
Visit levels J and M and H: 0.34.
Find the probabilities that a person visiting the temple will:
A. Visit level M given that he will go to level J.
B. Visit level H given that he will go to level J and level M.
C. Not visit level J given that he will visit level M and/or visit
level H.
D. Visit level H and visit level J given that he will not visit level
M.

Answer 1

a)

P(M|J)=P(M and J)/P(J) = 0.52/0.74=0.7027

b)      
P(H|(J and M)) = P(J and M and H)/P(J and M) = 0.34/0.52=   0.653846154  
      
c) P(not visit J|level M and H) = P(M and H and not J)/P(M and H) = (0.44-0.34)/0.44=   0.227272727  
      
P(not visit J|level M or H) =      
P(M or H)=P(M)+P(H)-P(M and H) = 0.70+0.62-0.44=   0.88  
      
P(vist J and (visit M or H)=0.52+0.46-0.34=   0.64  
P(not visit J and visit M or H) = (0.88-0.64)/0.64=   0.375  
      
D)      
P(not visit M)=1-0.70=   0.3  
      
P(Visit H and J and not Visit M ) = 0.46-0.34=   0.12  
      
P(Visit level H and visit level J given that he will not visit level M)=0.12/0.3= 0.4