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

Answer:

0.272

Step-by-step 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