How does level of affluence affect health care? In order to address one dimensio

Question

How does level of affluence affect health care? In order to address one dimension of the problem, a group of heart attack victims was drawn. Each was categorized as a low, medium, or high income earner. Each was also categorized as having survived or died. A demographer noted that in a certain country 21% fall into the low income group, and 49% in the medium income group. Furthermore, an analysis of heart attack victims in the same country reveals that 12% of low income people, 9% of medium income people, and 7% of high income people die of heart attacks. Name the random variables in this problem. List the values assumed by each random variable. What is the probability that a person chosen at random in the country will fall in the high income group? A person chosen at random was classified as a survivor of a heart attack. Find the probability that this person comes from the low income group a. b. c. d.

Explanation / Answer

(a)

Variables are:

Variable 1: Income group

Variable 2: Survived or died

b)

Variable: Income group

Values it can take: Low, high and medium

Variable: Survived or died

Values it can take: Survived or died

c)

From the given information we have

P(low) = 0.21, P(medium) = 0.49

By the complement rule:

P(high) = 1 - P(low) - P(medium) =1 - 0.21 - 0.49 = 0.30

(d)

Let S shows the event that person classified as a survivor of heart attack and D shows the event that person classified as died of heart attack. So we have

P(D | low) = 0.12, P(D | medium) = 0.09, P(D | high) = 0.07

By the complement rule,

P(S | low) = 1-P(D|low) =0.88 , P(S | medium) =1-P(D|medium) = 0.91, P(S | high) =1-P(D|high)= 0.93

By the Bayes theorem,

P(low |S) = [ P(S|low)P(low) ] / [P(S|low)P(low)+P(S| medium)P(medium)+P(S| high)P(high)] =[ 0.88 *0.21 ] / [ 0.88 *0.21 + 0.91 * 0.49 + 0.93 * 0.30] = 0.0252 / 0.0903 = 0.2031

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