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

• MHB
• Collins1
In summary, by calculating the joint probabilities of male and female customers buying the ABC set of books, we can determine that the probability of meeting a male customer is approximately 65.2% and the probability of meeting a female customer is approximately 34.8%. These probabilities are based on the assumption that the average frequency of shopping is once a week and the ratio of male to female customers is 3 to 1.
Collins1
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.

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 $$\frac{4125}{6125}= 0.673 and the probability the person is female is [tex]\frac{2000}{6125}= 0.327$$.

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 $$\frac{1875}{2875}= 0.652 and the probability the person is female is [tex]\frac{1000}{2875}= 0.348$$.

If you meant that, of the men, "15% buy book D at least once in a week" rather than "month" 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 $$\frac{1625}{2750}= 0.591$$.

## 1. What is conditional probability?

Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of both events occurring by the probability of the first event occurring.

## 2. How do you calculate conditional probability?

To calculate conditional probability, you need to know the probability of both events occurring and the probability of the first event occurring. The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the conditional probability of A given B, P(A and B) is the probability of both A and B occurring, and P(B) is the probability of B occurring.

## 3. What is the significance of calculating conditional probability in marketing?

Calculating conditional probability in marketing allows businesses to understand the relationship between different events or factors and how they affect consumer behavior. This can help businesses make more informed decisions about their marketing strategies and target specific groups of customers more effectively.

## 4. How can conditional probability be used to analyze male and female customers' buying habits?

Calculating conditional probability can be used to analyze male and female customers' buying habits by looking at the probability of each gender buying certain products or product categories. This information can then be used to tailor marketing campaigns and promotions to better appeal to each gender and increase sales.

## 5. What are some limitations of using conditional probability to analyze customer behavior?

One limitation of using conditional probability to analyze customer behavior is that it only looks at the relationship between two events or factors, and does not take into account other potential factors that may influence behavior. Additionally, the data used to calculate conditional probability may not be representative of the entire population, leading to biased results.

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