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At a prestigious country club, 60% of members are men and 40% of members are female....

At a prestigious country club, 60% of members are men and 40% of members are female. On average, 2 members die every month. Whenever a member dies, their name is placed on a wall. Due to the wall being small, there is to only be one name on the wall at a time. When someone dies, the current name on the wall is replaced by the newly deceased's. Today is January 1st and a women just died. What is the probability that on January 15th, the name on the wall is still a woman's? (does not have to be the same name.)

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