The percentage of all miners in the sample who are non-smokers is 48%, the percentage of all miners in the sample who smoke less than one pack a day is 21%, and the percentage of all miners in the sample who smoke one or more pack a day is 24%. Amongst all non-smokers, 25% have been diagnosed with lung cancer. Amongst all smokers of less than one pack a day, 33% have been diagnosed with lung cancer. Amongst all smokers of one or more pack a day, 63% have been diagnosed with lung cancer. Use this information to answer question 8.
1. Fill in the table, the joint distribution of smoking behavior and lung cancer diagnoses for the sample of miners. Round all answers to four digits. Show all work.
non-smoker
diagnosed with lung cancer
No diagnosis of lung cancer
Total 1.00
A study was conducted to evaluate the relationship between cause of death (denoted by the letter D) and smoking habits (denoted by the letter S) in China. The researchers composed the following joint probability table showing the probabilities based on cause of death and smoking habits. Use this information to answer question 9.
cause of death and smoking smoker(s) non- smoker (s')
lung cancer(D1) 0.051 0.051
cardiovascular disease (D2) 0.119 0.213
other(D3) 0.171 0.395
2. If I were to select a random person from China who has died, calculate the following probabilities (15%):
a. The person's cause of death was lung cancer
b. The person's cause of death was CVD and the person was a non-smoker
c. The person was a non-smoker
d. The person died of other causes given the person was a smoker
e. P(D3)
f. P(S|D1)