The Language of Argument

2 4 6

C HaP Te r 1 1 ■ C h a n c e s

Some Rules of Probability

Suppose you have determined the probability that certain simple events

will occur; how do you go about applying this information to combinations

of events? This is a complex question and one that can be touched on only

lightly in this text. There are, however, some simple rules of probability

that are worth knowing because they can guide us in making choices when

outcomes are uncertain.

Probabilities of Negations

By convention, events are assigned probabilities between 0 and 1 (inclusive).

An event is going to either occur or not occur; that, at least, is certain (that is,

it has a probability of 1). From this it is easy to see how to calculate the proba-

bility that the event will not occur, given the probability that it will occur: We

simply subtract the probability that it will occur from 1. This is our first rule:

Rule 1: Negation. The probability that an event will not occur is 1 minus

the probability that it will occur. Symbolically:

Pr(not h) 5 1 2 Pr(h)

For example, the probability of drawing an ace from a standard deck is one

in thirteen, so the probability of not drawing an ace is twelve in thirteen.

Using the above chart, answer the following questions about the total on throw

of two dice:

1. What is the probability of throwing a five?


2. Which number has the highest probability of being thrown? What is its
   probability?


3. What is the probability of throwing an eleven?


4. What is the probability of throwing either a seven or an eleven?


5. Which is more likely: throwing either a five or an eight?


6. Which is more likely: throwing a five or an eight, or throwing a two or a
   seven?


7. What is the probability of throwing a ten or above?


8. What is the probability of throwing an even number?


9. What is the probability of throwing an odd number?


10. What is the probability of throwing a value from four to six?


11. What is the probability of throwing either a two or a twelve?


12. What is the probability of throwing a value from two to twelve?

exercise i

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