Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 82 people in the 18-21 age bracket and finds that 70 of them respond and 12 refuse to respond. When 296 people in the 22-29 age bracket are contacted, 272 respond and 24 refuse to respond. Assume that 1 of the 378 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

Answer 1

`(366)/(378)`

Explanation:

The given information is summarized in the table below.

`\left|\begin{array}c$Age Bracket&$Respond&$Refuse to respond&$Total\\18-21&70&12&82\\22-29&272&24&296\\--&--&--&--\\$Total&342&36&378\end{array}\right|`

Probability of getting someone in the 22-29 age bracket = 296/378

Probability of getting someone who agreed to respond = 342/378

Probability of both = 272/378

Therefore:

The probability of getting someone in the 22-29 age bracket or someone who agreed to respond

`=(296)/(378) +(342)/(378) -(272)/(378) \\\\=(366)/(378) \\\\=0.9683`