Help to understand the disjunction fallacy

www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/79/Disjunction-Fallacy

I am having trouble grasping the disjunction fallacy. I understand the concept of it, but I can't imagine when people would actually be making this mistake.

The examples given seem forced, as though they were designed by researchers to trip people up. I would never look at a bloke in the street and wonder "Is it more likely that he is a basketballer, or that he is either a basketballer or a jockey?"

Is there an example of a person committing the disjunction fallacy in an everyday situation, or in a real argument, rather than in response to a contrived scenario/quiz question?

Thank you,
Sarah

Case in point. Many people will scoff at the idea of "magic." If an adult were to say the universe appeared by magic, others would likely see that person as having some kind of intellectual disability. However, if one were to say that the universe is here by God (like billions of people do), others wouldn't flinch. What is God? Magic + other characteristics. So what is more likely to exist... God or magic? Most people would say God, but the logical answer is magic. This is the disjunction fallacy in action.

I will try to make some.

My car was broken into... What is more likely? The thief was a homeless guy? Or the thief was a homeless guy who was on crack? It was more likely a homeless guy because there are more homeless guys than homeless guys who are also on crack.

The phone rings... What is more likely? The caller is a woman? Or the caller is a woman calling about the money you owe the IRS? It is more likely a woman because there are more women than women collecting taxes.

What is more likely? A man taking a woman? Or a man talking to a beautiful woman? Beautiful women are women so he is more likely talking to a woman.

We encounter this fallacy quite often. You must either be a Democrat or a Republican - wrong, there are other choices. You must buy this car now or it will be gone and you won't be able to get a car - wrong.

But it's not always a fallacy. Sometimes there are only two choices.