The American Cancer Society is planning to mail out questionnaires concerning br

Question

The American Cancer Society is planning to mail out questionnaires concerning breast cancer. From past experience with questionnaires, the Society knows that only 15 percent of the people receiving questionnaires will respond. It also knows that 1.3 percent of the questionnaires mailed out will have a mistake in address and never be delivered, that 2.8 percent will be lost or destroyed by the post office, that 19 percent will be mailed to people who have moved, and that only 48 percent of those who more leave a forwarding address. What is the probability that the Society will receive a reply from a given questionnaire?

Explanation / Answer

Here,

P(will receive the questionnaire) = 1 - P(mistake in address) - P(destroyed) - P(moved) P(no forwarding adress|moved)

Thus,

P(will receive the questionnaire) = 1 - 0.013 - 0.028 - 0.19*(1-0.48) = 0.8602

Thus,

P(will answer) = P(will receive the questionnaire) P(will answer|received the questionnaire)

P(will answer) = 0.8602*0.15

= 0.12903 [ANSWER]

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