MHB Calculating Conditional Probability of Male/Female Customers Buying Books A-D

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The discussion focuses on calculating the conditional probabilities of male and female customers buying books A, B, and C in a bookshop with a male-to-female customer ratio of 3 to 1. It details the weekly purchase percentages for each book among male and female customers, leading to the conclusion that for book A, the probability a buyer is male is approximately 0.652, while for females it is about 0.348. For book B, the male probability is around 0.673 and female probability is about 0.327. For book C, the probabilities are similar to book A, with males at approximately 0.652 and females at 0.348. The discussion also touches on the relevance of shopping frequency and the inclusion of book D in the calculations.
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There are 4 books being sold in the bookshop : A, B, C, D.

We know that 20% of the male customers buy book A at least once a week, 55% buy book B at least once a week, 25% buy book C at least once a week and 15% buy book D at least once in a month.

We also know that 32% of the female customers by book A at least once a week, 80% buy book B at least once a week, 40% buy book C at least once a week and 65% buy book D at least once a week.

The ratio of male customers to female is 3 to 1.

The goal is to calculate a probability of meeting male and a female in the shop, given that each customer decided to purchase books A, B, C and the average frequency of shopping is once a week.
I believe the solution is to calculate joint probability of male and female probabilities of buying ABC set. Maybe I'm wrong so I could use some help. Also I'm not sure if shopping frequency matters.
 
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I thought I had already answered this. Did you ask it on another forum?

Yes, "the average frequency of shopping is once a week" matters because we are told how many of books A, B, and C are bought a week. (We are told the number of books, D, are bought in a month, but the question doesn't ask about "D".)

Imagine 10000 customers. "The ratio of male customers to female is 3 to 1." So there are (3/4)(10000)= 7500 male customers and 2500 female customers.

"We know that 20% of the male customers buy book A at least once a week, 55% buy book B at least once a week, 25% buy book C at least once a week and 15% buy book D at least once in a month."
So of the male customers 0.20(7500)= 1500 buy book A, 0.55(7500)= 4125 buy book B, 0.25(7500)= 1875 buy book C, and 0.15(7500)= 1125 buy book D.

"We also know that 32% of the female customers buy book A at least once a week, 80% buy book B at least once a week, 40% buy book C at least once a week and 65% buy book D at least once a week."
So of the female customers 0.32(2500)= 800 buy book A, 0.80(2500)= 2000 buy book B, .4(2500)= 1000 buy book C, and .65(2500)= 1625 buy book D.A total of 1500+ 800= 2300 buy book A, 1500 of them men, 800 or them women. Given that a person buys book A the probability the person is male is \frac{1500}{2300}= 0.652 (rounded) and the probability the person is female is \frac{800}{2300}= 0.348. Of course, 0.348= 1- 0.652.

A total of 4125+ 2000= 6125 buy book B, 4125 of them men, 2000 of them women . Given that a person buys book B the probability the person is male is \frac{4125}{6125}= 0.673 and the probability the person is female is \frac{2000}{6125}= 0.327.<br /> <br /> A total of 1875+ 1000= 2875 buy book C, 1875 of them men, 1000 of them women . Given that a person buys book C the probability the person is male is \frac{1875}{2875}= 0.652 and the probability the person is female is \frac{1000}{2875}= 0.348.&lt;br /&gt; &lt;br /&gt; If you &lt;b&gt;meant&lt;/b&gt; that, of the men, &amp;quot;15% buy book D at least once in a &lt;b&gt;week&lt;/b&gt;&amp;quot; rather than &amp;quot;month&amp;quot; and intended to include people who bought book D, then a total of 1125+ 1625= 2750 buy book D, 1125 of them men, 1625 of them women. Given that a person buys book D, the probability the customer is a man is \frac{1125}{2750}= 0.409 and the probability the customer is a woman is \frac{1625}{2750}= 0.591.
 
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