Page 155 and 157: Definitions/uses of terms "outcome" and "state" swapped

[chrisoffner]

Describe the mistake On page 155 (of the paperback print edition) the book reads

The sample space is the set of all possible outcomes of the experiment, usually denoted by Ω.

as well as

In this book, we refer to T as the target space and refer to elements of T as states. We introduce a function X : Ω → T that takes an element of Ω (an outcome) and returns a particular quantity of interest x, a value in T . This association/mapping from Ω to T is called a random variable.

But then on page 157, the usage of the terms appears to be swapped:

Via the random variable X, which maps states to outcomes, we see in the right-hand side of (6.8) that this is the probability of the set of states (in Ω) that have the property (e.g., $£, £$).

Location

1. Version: Paperback print (3rd printing 2020)
2. Chapter: 6.1.2
3. 155 and 157
4. page 155, lines 4, 17, page 157, lines 3, 4

Proposed solution On page 157, swap the highlighted occurrences of "state" and "outcome". A random variable X maps an outcome (ω ∊ Ω) to a state (x ∊ T).

Additional context In the PDF the excerpts in question are on pages 175 and 177, respectively.

[blargoner]

This error still exists as of version 2024-01-15 of the PDF and is not limited to the example given. For example, on p. 175 immediately after introducing the concept of a random variable, we see

For example, in the case of tossing two coins and counting the number of heads, a random variable X maps to the three possible outcomes: ...

On p.177 we have

...for example, a single element of T, such as the outcome that one head is obtained when tossing two coins...

and

The left-hand side of (6.8) is the probability of the set of possible outcomes (e.g. number of $ = 1) that we are interested in.

and

...P_X, which defines the probability mapping between the event and the probability of the outcome of the random variable.

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Relatedly in Example 6.1 on p. 176, states are also being referred to as "events":

The event we are interested in is the total number of times the repeated draw returns $.

and

Note that there are two experimental outcomes, which map to the same event...

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This kind of sloppiness is bound to cause needless confusion for the uninitiated. The authors note on p. 174 that they are being "lazy" with notation and jargon, and acknowledge that this can be confusing. My question is, why bother writing a book intended to be accessible to newcomers if one is planning to be lazy and confusing?