Bayes Theorem, The Law of Total Probability, and Trees that Don't Grow.

Question

" A doctor is concerned about the relationship between blood pressure and irregular heartbeats. Among her patients, she classifies blood pressures as high, normal, or low and heartbeats as regular or irregular and finds that (a) 16% have high blood pressure; (b) 19% have low blood pressure; (c) 17% have an irregular heartbeat; (d) of those with an irregular heartbeat, 35% have high blood pressure; and (e) of those with normal blood pressure 11% have an irregular heartbeat. What percentage of her patients have a regular heartbeat and low blood pressure?"

How could I explain this problem using a tree? This is what I have so far

Answer 1

Hints:

You can calculate Pr(High blood pressure and irregular heat beat), the penultimate lower branch of your tree, from:

"(c) 17% have an irregular heartbeat; (d) of those with an irregular heartbeat, 35% have high blood pressure"

With your other information, that will enable you to calculate

• Pr(High blood pressure and regular heat beat)
• Pr(Low blood pressure and irregular heat beat)

and thus

• Pr(Low blood pressure and regular heat beat)

so giving you figures for all the branches of your tree