Question

To ascertain the effectiveness of the advertising campaign for the Red Cross Annual Appeal on donations, a telephone survey of 302 Brisbane residents was conducted. Two of the questions asked were

1. Did you see the advertisement for the Annual Appeal?
2. Did you donate to the Appeal?

193 of the survey respondents indicated they saw the advertisement for the Annual Appeal. Of these 193 respondents, 11 of them indicated that they did not donate to the Annual Appeal. Overall, 71 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)

Answer 1

The response matrix is as follows.

	Saw Advertisement	Did not see Advertisement	Total
Donated	193 - 11 = 182	109 - 60 = 49	302 - 71 = 231
Did not donate	11	71 - 11 = 60	71
Total	193	302 - 193 = 109	302

Probability that a random respondent donated or saw the advertisement = Probability that she donated + Probability that she saw advertisement - Probability that she donated and saw the advertisement

= (231 / 302) + (193 / 302) - (182 / 302)

= (231 + 193 - 182) / 302

= 242 / 302

= 0.801