A belief network models the relation between the variables oil price (oil), inflation rate (inf), economy health (eh), British Petroleum (BP) Stock price (bp), retailer stock price (rt). Each variable takes the states low, high, except for bp which has states low, high, normal. The belief network model for these variables has the table below.

p(eh=low)=0.2
p(bp=low | oil=low)=0.9 p(bp=low | oil=high)=0.1 p(oil=low | eh=low)=0.9 p(rt=low | inf=low, eh=low)=0.9 p(rt=low | inf=high, eh=low)=0.1 p(inf=low | oil=low, eh=low)=0.9 p(inf=low | oil=high, eh=low)=0.1	p(bp=normal | oil=low)=0.1 p(bp=normal | oil=high)=0.4 p(oil=low | eh=high)=0.5 p(rt=low | inf=low, eh=high)=0.1 p(rt=low | inf=high, eh=high)=0.01 p(inf=low | oil=low, eh=high)=0.1 p(inf=low | oil=high, eh=high)=0.01

a) Draw a belief network for this distribution.

b) Given that the BP stock price is normal and the retailer stock price is high, what is the probability that inflation is high?