A public good is that type of good that cannot be provided in a free market for if it is provided the market will fail. While a private good is that type of good which can be provided in a market at a price.

Principle characteristics of public goods include the following:

1. Non-excludability. This means that when one consumes a public good, you don't exclude others from consuming the same.
2. Non-rivals. This means that when someone consumes a public good, it doesn't diminish. In other words, other consumers don't have a less of an amount to consume.

Principle characteristics of a private good include the following:

1. Excludability. Meaning that when one consumes private goods, other consumers are excluded from consuming the same product. Let's say you're eating a mango: this means that the mango that's being consumed is no longer available to any other person for their own consumption.
2. Rivalness. A public good is rival in that when one consumes a private good, a lesser amount is available to be consumed by other consumers.

So yes, there is a free rider problem in public good. A 'free rider problem' is a condition where people take advantage of using a common resource and thus no one is willing to pay for the usage of the good. The reason why there is a problem of a free rider is that it's not possible to set a price on public goods. For example, it's not possible to set a price on people who drive on a road.

A local police force service is an example of a public good because it doesn't have a price tag and my consumption of police force services don't exclude other consumers from consuming the same services.

A local TV service is an example of a private good because though it is accessible by many people, there is a price tag for accessing the same meaning that if you don't pay the subscription, then you won't watch any channels that is the concept of excludability.