Problem

Of the 35 plays attributed to a playwright, 13 are comedies, 10 are tragedies, and 12 are histories. If one play is selected at random, find the odds in favor of selecting a history or a tragedy.
The odds in favor are
(Simplify your answer.)

Answer

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Answer

Final Answer: The odds in favor of selecting a history or a tragedy are approximately \(\boxed{1.69}\).

Steps

Step 1 :Define the total number of plays, which is 35.

Step 2 :Define the number of comedies, which is 13.

Step 3 :Define the number of tragedies, which is 10.

Step 4 :Define the number of histories, which is 12.

Step 5 :Calculate the number of favorable outcomes, which is the sum of the number of histories and tragedies. So, \(favorable\_outcomes = histories + tragedies = 10 + 12 = 22\).

Step 6 :Define the number of unfavorable outcomes, which is the number of comedies. So, \(unfavorable\_outcomes = comedies = 13\).

Step 7 :Calculate the odds in favor, which is the ratio of the number of favorable outcomes to the number of unfavorable outcomes. So, \(odds\_in\_favor = \frac{favorable\_outcomes}{unfavorable\_outcomes} = \frac{22}{13} = 1.6923076923076923\).

Step 8 :The odds in favor of selecting a history or a tragedy is approximately 1.69. This means that for every 13 comedies, there are approximately 1.69 times as many histories or tragedies.

Step 9 :Final Answer: The odds in favor of selecting a history or a tragedy are approximately \(\boxed{1.69}\).

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