Question

1. In an experiment to study the relationship of hypertension and smoking habits, the following data below are collected for 180 individuals, where H and NH in the table stands for Hypertension and Non-hypertension, respectively. If one of these individuals is selected at random, find the probability that the person is:

(a) not experiencing hypertension, given that the person is a heavy smoker
(b) a nonsmoker, given that the person is not experiencing hypertension
(c) either a moderate or heavy smoker, given that the person is not experiencing hypertension

Answer 1

We have the following dara

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c:c } & Nonsmokers & Moderate\ & Heavy & Total \\ & & smokers & smokers & \\ \hline H & 21 & 36 & 30 & 87 \\ NH & 48 & 26 & 19 & 93 \\ \hdashline Total & 69 & 62 &49 & 180 \end{array}$$

where H and NH stands for Hypertension and NonHypertension, respectively.

Let $N_S$ denotes the nonsmoker, $M_S$ denotes the moderate smoker, and $H_S$ denotes the heavy smoker.

One of these inividuals is selected at random.

a)

$$P(NH|H_S)=\dfrac{19}{49}$$

b)

$$P(N_S|NH)=\dfrac{48}{93}=\dfrac{16}{31}$$

c)

$$P((M_S\cup H_S)|NH)=\dfrac{26+19}{93}=\dfrac{15}{31}$$