1. ## Probability 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?

I would appreciate any help in solving this, as I am confused!

2. Hello,

I'd suggest you draw a Venn diagram

3. Hello.

Thank you for your suggestion. However, I still have a hard time finding the answer. I suspect I may have to use the Bayes's Theorem here since this chapter section is about this, but can't see how to proceed with the information given.

4. Originally Posted by krje1980
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?

I would appreciate any help in solving this, as I am confused!
There are many ways to do this. Since I'm hopeless with probability formulas I'll draw a Karnaugh table:

$\displaystyle \begin{tabular}{l | c | c | c | c} & High & Normal & Low & \\ \hline Regular & a & b & c & h \\ \hline Irregular & d & e & f & 0.17 \\ \hline & 0.16 & g & 0.19 & 1 \\ \end{tabular}$

It's clear that g = 0.65 and h = 0.83.

From (d): $\displaystyle \frac{d}{0.16} = 0.35 \Rightarrow d = 0.056$

From (e): $\displaystyle \frac{e}{g} = \frac{e}{0.65} = 0.11 \Rightarrow e = 0.0715$.

Update the Karnaugh Table:

$\displaystyle \begin{tabular}{l | c | c | c | c} & High & Normal & Low & \\ \hline Regular & a & b & c & 0.83\\ \hline Irregular & 0.056 & 0.0715 & f & 0.17 \\ \hline & 0.16 & 0.65 & 0.19 & 1 \\ \end{tabular}$

Your task is to calculate the value of c (treat it like a Sodoku puzzle).