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To ascertain the effectiveness of the advertising campaign for the Red Cross Annual Appeal on donations, a telephone survey of 296 Brisbane residents was conducted. Two of the questions asked were1.  Did you see the advertisement for the Annual Appeal?2.  Did you donate to the Appeal?202 of the survey respondents indicated they saw the advertisement for the Annual Appeal. Of these 202 respondents,  12 of them indicated that they did not donate to the Annual Appeal. Overall, 82 respondents did not donate to the Appeal. One of the respondents from the survey was chosen at random. What is the probability that this respondent donated to the Annual Appeal or saw the Annual Appeal advertisement? (3 decimal places)

Question

To ascertain the effectiveness of the advertising campaign for the Red Cross Annual Appeal on donations, a telephone survey of 296 Brisbane residents was conducted. Two of the questions asked were1.  Did you see the advertisement for the Annual Appeal?2.  Did you donate to the Appeal?202 of the survey respondents indicated they saw the advertisement for the Annual Appeal. Of these 202 respondents,  12 of them indicated that they did not donate to the Annual Appeal. Overall, 82 respondents did not donate to the Appeal. One of the respondents from the survey was chosen at random. What is the probability that this respondent donated to the Annual Appeal or saw the Annual Appeal advertisement? (3 decimal places)

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Solution

First, let's find out how many people donated to the Annual Appeal.

We know that 82 respondents did not donate to the Appeal. So, the number of people who donated to the Appeal is the total number of respondents minus those who did not donate:

296 (total respondents) - 82 (did not donate) = 214 (donated)

Next, we need to find out how many people either donated to the Appeal or saw the advertisement.

We know that 202 respondents saw the advertisement and 214 respondents donated. However, we can't simply add these two numbers together because some people both saw the advertisement and donated. We know that 12 of the 202 people who saw the advertisement did not donate, so 202 - 12 = 190 people both saw the advertisement and donated.

So, the number of people who either saw the advertisement or donated is:

202 (saw the ad) + 214 (donated) - 190 (both) = 226

Finally, we can find the probability that a randomly chosen respondent either saw the advertisement or donated to the Appeal by dividing the number of people who either saw the ad or donated by the total number of respondents:

226 / 296 = 0.763 (rounded to three decimal places)

So, the probability that a randomly chosen respondent either saw the advertisement or donated to the Annual Appeal is 0.763.

This problem has been solved

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