MHB Male Customers Preferring Non-Fiction: Proving Independence

[tmt1]

Given the scenario that a bookstores customers is 40% male and 50% of male customers prefer non-fiction, what is the probability that a customer is male and prefers non-fiction.

So, since being male and preferring non-fiction are independent, we can multiply them and get 20%.

How can we prove that they are independent?

 

[I like Serena]

Given the scenario that a bookstores customers is 40% male and 50% of male customers prefer non-fiction, what is the probability that a customer is male and prefers non-fiction.

So, since being male and preferring non-fiction are independent, we can multiply them and get 20%.

How can we prove that they are independent?

Hi tmt,

We can't. We do not have enough information.
They would be independent if we knew for instance that 50% of female customers preferred non-fiction, but that is not given.

Note that the 50% is a conditional probability - it's the probability a customer prefers non-fiction given that he is male.
So we're calculating:
$$P(\text{male AND non-fiction}) = P(\text{non-fiction} \mid \text{male}) \ P(\text{male})$$

 

[HallsofIvy]

Notice that what you are given is not "the probability a customer will choose non-fiction is 50%". What you are given is that "the probability a customer will choose non-fiction, given that the customer is male, is 50%". That is, taking M for "the customer is male" and N for "the customer chooses non-fiction", you are told that "P(N|M)= 0.50". And, whether M and N are independent or not P(M and N)= P(M)*P(N|M).