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$19,077 \times \mathrm{XP}$
- Jakai Matthews
Bookwork code: G24
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Georgia works at a book shop. She finds that when a book is chosen from the shop at random, the following probabilities are correct:
\[
\begin{array}{c}
P(\text { fiction })=0.34 \\
P(\text { paperback })=0.23 \\
P(\text { both fiction and paperback })=0.16
\end{array}
\]
Work out $P$ (neither fiction nor paperback) as a decimal.
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Answer
\(\boxed{P(\text{neither fiction nor paperback}) = 0.59}\)
Step 1 ：Given probabilities: \(P(\text{fiction}) = 0.34\), \(P(\text{paperback}) = 0.23\), and \(P(\text{both fiction and paperback}) = 0.16\)
Step 2 ：Calculate the probability of a book being fiction or paperback: \(P(\text{fiction or paperback}) = P(\text{fiction}) + P(\text{paperback}) - P(\text{both fiction and paperback}) = 0.34 + 0.23 - 0.16 = 0.41\)
Step 3 ：Calculate the probability of a book being neither fiction nor paperback: \(P(\text{neither fiction nor paperback}) = 1 - P(\text{fiction or paperback}) = 1 - 0.41 = 0.59\)
Step 4 ：\(\boxed{P(\text{neither fiction nor paperback}) = 0.59}\)
