Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 101 people in the 18-21 age bracket and finds that 86 of them respond and 15 refuse to respond. When 266 people in the 22-29 age bracket are contacted, 238 respond and 28 refuse to respond. Assume that 1 of the 367 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond.

Answer 1

The probability of getting someone in the 18-21 age bracket or someone who agreed to respond is 0.6757.

Explanation:

The data provided is summarized in the table below.

The probability of randomly selecting a person, from the 367 people, in the age group 18-21 or someone who agreed to respond is:

P (A person in the age group 18-21 OR agreed to respond)

= P (A person in the age group 18-21) + P (A person agreed to respond)

- P (A person in the age group 18-21 AND agreed to respond)

`=(101)/(367)+(324)/(367)-(86)/(367)`

`=(101+324-86)/(367)\\`

`=(248)/(367)`

`=0.6757`

Thus, the probability of getting someone in the 18-21 age bracket or someone who agreed to respond is 0.6757.