A bookstore sells books in several formats- hardcover,...

A bookstore sells books in several formats- hardcover, paperback, digital, and audio. Based on past sales, the table below gives the estimated probabilities that a randomly selected purchase will be of particular types. $$ \begin{array}{|cccc|} \hline \text { Hardcover } & \text { Paperback } & \text { Digital } & \text { Audio } \\ \hline 0.16 & 0.36 & 0.40 & 0.08 \\ \hline \end{array} $$ If a purchase is selected at random, what is the probability that this purchase is for a book that is a. digital or audio? b. not digital? c. a printed book?

A bookstore sells books in several formats- hardcover, paperback, digital, and audio.
Based on past sales, the table below gives the estimated probabilities that a randomly selected purchase will be of particular types.
$$
\begin{array}{|cccc|}
\hline \text { Hardcover } & \text { Paperback } & \text { Digital } & \text { Audio } \\
\hline 0.16 & 0.36 & 0.40 & 0.08 \\
\hline
\end{array}
$$
If a purchase is selected at random, what is the probability that this purchase is for a book that is
a. digital or audio?
b. not digital?
c. a printed book?

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Key Concepts

Probability

Probability is a measure quantifying the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. In probability, the sum of the probabilities of all mutually exclusive outcomes in a sample space is 1.

Mutually Exclusive Events

Mutually exclusive events are events that cannot occur simultaneously. In probability problems, when dealing with outcomes that cannot happen at the same time, the probability of one or another occurring is the sum of their individual probabilities.

Addition Rule for Probabilities

The addition rule is used to calculate the probability that at least one of multiple mutually exclusive events occurs. For mutually exclusive events, the probability of their union is simply the sum of their individual probabilities, making it a fundamental tool for combining probabilities for events like different types of purchases.

Complement Rule

The complement rule states that the probability of an event not occurring is equal to one minus the probability that it does occur. This rule is useful when it is easier to calculate the probability of the event happening rather than not happening, allowing one to determine the probability of the complementary event.

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