This chapter explains the usual notation for talking about probability, and then reminds you how to add and multiply with probabilities.
WHAT HAS A PROBABILITY?
Suppose you want to take out car insurance. The insurance company will want to know your age, sex, driving experience, make of car, and so forth. They do so because they have a question in mind:
What is the probability that you will have an automobile accident next year?
That asks about a proposition (statement, assertion, conjecture, etc.):
“You will have an automobile accident next year.”
The company wants to know: What is the probability that this proposition is true?
The insurers could ask the same question in a different way:
What is the probability of your having an automobile accident next year?
This asks about an event (something of a certain sort happening). Will there be “an automobile accident next year, in which you are driving one of the cars involved”?
The company wants to know: What is the probability of this event occurring?
Obviously these are two different ways of asking the same question.
PROPOSITIONS AND EVENTS
Logicians are interested in arguments from premises to conclusions. Premises and conclusions are propositions. So inductive logic textbooks usually talk about the probability of propositions.
Most statisticians and most textbooks of probability talk about the probability of events.
So there are two languages of probability, propositions and events.
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