Question 1182125: Pollsters are concerned about declining levels of cooperation among persons contacted in surveys.
A pollster contacts 76 people in the 18-21 age bracket and finds that 65 of them respond and 11 of them refuse to respond.
When 303 people in the 22-29 age bracket are contacted, 283 respond and 20 refuse to respond.
Assume that 1 of the 379 people is randomly selected.
Find the probability of getting someone in the 18-21 age bracket or someone that does not respond.
Answer to a percent rounded to 1 decimal.
Answer by math_tutor2020(3817)   (Show Source):
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Table:
| Response | No response | Total | | Age 18 to 21 | 65 | 11 | 76 | | Age 22 to 29 | 283 | 20 | 303 | | Total | 348 | 31 | 379 |
Define the two events
A = someone is in the 18-21 age bracket
B = the person does not respond
Based on the table, we have
n(A) = number of people in set A = 76
n(B) = 31
n(A and B) = 11
So,
n(A or B) = n(A) + n(B) - n(A and B)
n(A or B) = 76+31-11
n(A or B) = 96
We have 96 people in the age 18-21 bracket, they didn't respond, or both.
Divide this over the 379 people surveyed
96/379 = 0.253 = 25.3%
Answer: 25.3%
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