Recall the following example from Unit 3 Module 5:


EXAMPLE 3.5.1*
According to a recent article from the New England Journal of Medical Stuff , 63% of cowboys suffer from saddle sores, 52% of cowboys suffer from bowed legs, and 40% suffer from both saddle sores and bowed legs.

What is the probability that a randomly selected cowboy...
4. ...has saddle sores and bowed legs?
Let's answer this question again, using the Multiplication Rule for Independent events.
Let E be the event "the randomly selected cowboy has saddle sores." Then P(E) = .63. Let F be the event "the randomly selected cowboy has bowed legs." Then P(F) = .52. According to the multiplication rule,

This seems very nice, until we notice that the data provided in the problem states directly that P(E and F) = .40.
The question now is: What's wrong here? Why does the Multiplication Rule not give the correct answer?

Hint: There's nothing wrong with the Multiplication Rule For Independent Events. The fact that the Multiplication Rule doesn't give the "right answer" is just an indication that these events are not independent.
That is, a cowboy who has saddle sores is more likely to also have bowed legs. In a short while we will discuss the correct way to use the Multiplication Rule in cases like this involving DEPENDENT events.