As shown in Table 3-1, for very low probabilities, the odds are very close to the probability.

But as probability increases, the odds increase exponentially. By the time probability reaches 0.5,

the odds have become 1, and as probability approaches 1, the odds become infinitely large! This

definition of odds is consistent with its common-language use. As described earlier with the

casino example, if the odds of a horse losing a race are 3:1, that means if you bet on this horse,

you have three chances of losing and one chance of winning, for a 0.75 probability of losing.

TABLE 3-1 The Relationship between Probability and Odds

Probability Odds

Interpretation

1.0

Infinity The event will definitely occur.

0.9

9

The event will occur 90% of the time (it is nine times as likely to occur as to not occur).

0.75

3

The event will occur 75% of the time (it is three times as likely to occur as to not occur).

0.5

1.0

The event will occur about half the time (it is equally likely to occur or not occur).

0.25

0.3333 The event will occur 25% of the time (it is one-third as likely to occur as to not occur).

0.1

0.1111 The event will occur 10% of the time (it is 1/9th as likely to occur as to not occur).

0

0

The event definitely will not occur.

Some Random Thoughts about Randomness

When discussing probability, it is also important to define the word random. Like the word

probability, we use the word random all the time, and though we all have some intuitive concept of it,

it is hard to define with precise language. In statistics, we often talk about random events and random

variables. Random is a term that applies to sampling. In terms of a sequence of random numbers,

random means the absence of any pattern in the numbers that can be used to predict what the next

number will be.

The important point about the term random is that you can’t predict a specific outcome if a

random element is involved. But just because you can’t predict a specific outcome with random

numbers doesn’t mean that you can’t make any predictions about these numbers. Statisticians can

make reasonably accurate predictions about how a group of random numbers behave collectively,

even if they cannot predict a specific outcome when any randomness is involved.

Selecting Samples from Populations

Suppose that we want to know the average systolic blood pressure (SBP) of all the adults in a

particular city. Measuring an entire population is called doing a census, and if we were to do that and

calculate the average SBP in that city, we would have calculated a population parameter.

But the idea of doing a census to calculate such a parameter is not practical. Even if we somehow had