Question

of the 36 plays attributed to a playwright, 13 are comedies, 11 are tragedies, and 12 are histories. if one play is selected at random, find the odds against selecting a comedy. the odds against selecting a comedy are □□. (simplify your answer)

Explanation:

Step1: Calculate the number of non - comedy plays

The total number of plays is \(n = 36\), and the number of comedy plays is \(n_{comedy}=13\). The number of non - comedy plays \(n_{non - comedy}=36 - 13=23\).

Step2: Determine the odds against selecting a comedy

The odds against an event \(E\) (in this case, \(E\) is selecting a comedy) is given by the ratio of the number of unfavorable outcomes to the number of favorable outcomes.
The odds against selecting a comedy is \(\frac{n_{non - comedy}}{n_{comedy}}\). Substituting \(n_{non - comedy}=23\) and \(n_{comedy}=13\), we get the ratio \(23:13\).

Answer:

\(23:13\)