Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 77 people in the 18-21 age bracket and finds that 65 of them respond and 12 refuse to respond. When 301 people in the 22-29 age bracket are contacted, 275 respond and 26 refuse to respond. Assume that 1 of the 378 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond.

Answer 1

0.272

Explanation:

Given:

Age group Number of people Respond Refused to respond

18-21 77 65 12

22-29 301 275 26

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Total 378 340 38

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Now,

P (the probability of getting someone in the 18-21 age bracket or someone who agreed to respond)

= P ( 18-21 ) + P ( Refused to respond ) - P ( 18-21 and refused to respond)

=
`\frac{\textup{77}}{\textup{378}}` +
`\frac{\textup{38}}{\textup{378}}` -
`\frac{\textup{12}}{\textup{378}}`

=
`\frac{\textup{77 + 38 - 12}}{\textup{378}}`

=
`\frac{\textup{103}}{\textup{378}}`

= 0.272