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A total of 48 percent of the women and 37 percent of the
Chapter 3, Problem 19P(choose chapter or problem)
Problem 19P
A total of 48 percent of the women and 37 percent of the men who took a certain “quit smoking” class remained nonsmokers for at least one year after completing the class. These people then attended a success party at the end of a year. If 62 percent of the original class was male,
(a) what percentage of those attending the party were women?
(b) what percentage of the original class attended the party?
Questions & Answers
QUESTION:
Problem 19P
A total of 48 percent of the women and 37 percent of the men who took a certain “quit smoking” class remained nonsmokers for at least one year after completing the class. These people then attended a success party at the end of a year. If 62 percent of the original class was male,
(a) what percentage of those attending the party were women?
(b) what percentage of the original class attended the party?
ANSWER:
Step 1 of 2
Given a total of 48 percent of the women and 37 percent of the men.
Our goal is
a). We need to find the percentage of those attending the party were women.
b). We need to find the percentage of the original class attended the party.
Let M denotes the event a person who attends the party is male and
Let W denotes the person who attends the party is Female and E be the event that a person was smoke free for a year.
Then from the given information we know that.
P(E/M) = 0.37, P(M) = 0.62, P(E/W) = 0.48.
P(W) = 1-P(M)
P(W) = 1-0.62
P(W) = 0.38
Therefore, P(W) is 0.38.
a). We are asked to complete P(W/E) which by Bayes’ rule is given by
P(W/E) =
P(W/E) =
P(W/E) =
P(W/E) =
P(W/E) =
P(W/E) = 0.4429
Therefore, the percentage of those attending the party were women is 0.4429.