Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 8686 people in the 18-21 age bracket and finds that 4343 of them respond and 4343 refuse to respond. When 276276 people in the 22-29 age bracket are contacted, 258258 respond and 1818 refuse to respond. Suppose that one of the 362362 people is randomly selected. Find the probability of getting someone in the 18 dash 2118-21 age bracket or someone who respondedresponded.

0.9503

Step-by-step explanation:

First of all, there are some wrong figures in the original text. Because there is a total of 362362 people, the figures should be 86086 (people in the 18-21 age bracket), 43043 (people in the 18-21 age bracket who respond) and 43043 people in the 18-21 age bracket who refuse to respond. In the same way, because there are 276276 people in the 22-29 age bracket, it should be 18018 and not 1818 who refuse to respond in this subset of people. Now, let's define the following events:

R: a person respond

A: a person belongs to the 18-21 age bracket. So,

The number of people who respond is 43043 + 258258 = 301301, so

P (R) = 301301/362362 = 0.8315

P (A) = 86086/362362 = 0.2376

P (R | A) = 43043/86086 = 0.5

We are looking for P (A∪R) = P (A) + P (R) - P (A∩R),

P (A∩R) = P (R | A) P (A) = (0.5) (0.2376) = 0.1188, so,

P (A∪B) = 0.2376 + 0.8315 - 0.1188 = 0.9503