Question

of the 44 plays attributed to a playwright, 18 are comedies, 14 are tragedies, and 12 are histories. if one play is selected at random, find the odds against selecting a history or a tragedy. the odds against are □□ (simplify your answer)

Explanation:

Step1: Calculate the number of non - history and non - tragedy plays

The number of non - history and non - tragedy plays (comedies) is \(n = 18\).

Step2: Calculate the number of history or tragedy plays

The number of history or tragedy plays is \(m=14 + 12=26\).

Step3: Calculate the odds against

The odds against an event \(E\) (selecting a history or a tragedy) is given by the ratio of the number of non - favorable outcomes to the number of favorable outcomes.
The odds against \(=\frac{18}{26}=\frac{9}{13}\)

Answer:

\(9:13\)