Learn English – What’s wrong with “Most people in the country would like to own their house some day.”

It is an idiom. Another well-known combination of the same nature is "part and parcel". Both are used with singular verb forms.

I think you found a typo in your book! It should read: "What're (What are) the odds?"

Here are some other examples of plural nouns in English that don't have a singular equivalent but sometimes get conjugated as singular:

• Scissors
• Pants

Even though the singular conjugation is not correct it still shows up, especially in conversation. "Media" is a great example of this, since it is actually a plural of "medium" but almost never is used as a plural.