Answer to Question #142123 in Statistics and Probability for qwerty

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)

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