HW 6 Solutions
(Scored out of a possible of 6 points: 5 points for this problem, 1
point for doing the others.)
Chapter 15, #30: Suppose that 23% of adults smoke. It's known
that 57% of smokers and 13% of nonsmokers develop a certain lung condition
by age 60.
a) Explain how these statistics indicate that lung condition and smoking
are not independent.
If they were independent, P( Lung cond. | smoker) = P(Lung cond.). But
also, P(Lung cond. | Non-smoker) = P(Lung cond.).
This means that P(lung cond. | smoker) = P(lung cond. | non-smoker). However,
the first probability is .57 and the second is .13. Since they are not equal,
they cannot be independent.
b) P(condition) = ....
Write a tree. The first split is Smoke/ No smoke. P(S)
= .23 P(no smoker) = .77
From the smoke branch, there are two branches: condition/ no cond P(condition
| smoke) = .57 P(no condition | smoke) = .63
From the non-smoke branch, condition/ no condition P(condition
| no smoke) = .13 P(no condition | no smoker) = .87
To find P(condnition) we add up all branches that end in "condition"
P(condition) = P(smoke and condition) + P(no smoke and have condition)
= P(smoke)*P(condition | smoke) + P(no smoke) * P(condition | no smoke)
= .23 * .57 + .77*.13 = .2312