Of all the Sunny Club members in a particular city, 25% prefer swimming on weekends and 75% prefer swimming on weekdays. 10% of the members in the city prefer swimming on weekends and are female. 55% of the members in the city prefer swimming on weekdays and are female. What is the probability that a randomly selected club member is female, given that the person prefers swimming on weekends?

Question

mathmale · Answer

As soon as I see the words "given that," a big bell rings in my head and reminds me that this is a case of conditional probability.  Given that Event B has already happened, what is the probability that Event A will happen?

What most people do with the given data is to arrange it in what is called a "contingency table."  Have you ever drawn one of those before, or at least seen one used in class or in your online materials?

mathmale · Answer

Note the categories:  male and female; prefer swimming on weekdays and prefer swimming on weekends.  How would you organize this data neatly in a table?

anonymous · Answer

25/100 weekends
10/100 weekend female