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Suppose that a survey was carried out in New York, and each respondent was faced with the following two questions: (A) Is the last digit of your Social Security number odd? (B) Have you ever lied on an employment application? The second question is, of course, quite sensitive, and for various reasons we might expect that a number of people would not answer the question honestly, especially if their response were yes. To overcome this potential bias, respondents were asked to flip a coin and then to answer question (A) if the result was "head" and answer (B) otherwise. A yes response was given by 37% of all respondents. What is the probability that a respondent who was answering the sensitive question (i,e (B)), replied yes?

8. Suppose that a survey was carried out in New York, and each respondent was faced with the following two questions: (A) Is the last digit of your Social Security number odd? (B) Have you ever lied on an employment application? The second question is, of course, quite sensitive, and for various reasons we might expect that a number of people would not answer the question honestly, especially if their response were yes. To overcome this potential bias, respondents were asked to ip a coin and then to answer question (A) if the result was \"head\" and answer (B) otherwise. A yes response was given by 37% of all respondents. What is the probability that a respondent who was answering the sensitive question (i,e (B)), replied yes