To find the probability that the movie Michael selects is not a comedy, we first need to determine the total number of movies he has and then how many of those are not comedies.
Michael has:
- 3 action movies
- 4 comedies
- 5 dramas
First, let's calculate the total number of movies:
\[ \text{Total movies} = 3 + 4 + 5 = 12 \]
Next, we find the number of movies that are not comedies. Since there are 4 comedies, the number of non-comedy movies is:
\[ \text{Non-comedy movies} = \text{Total movies} - \text{Comedies} = 12 - 4 = 8 \]
Now, we can calculate the probability that the movie Michael selects is not a comedy:
\[ \text{Probability (not a comedy)} = \frac{\text{Non-comedy movies}}{\text{Total movies}} = \frac{8}{12} \]
To express this probability in simplest form, we can simplify the fraction \( \frac{8}{12} \):
\[ \frac{8}{12} = \frac{2}{3} \]
Thus, the probability that the movie Michael selects is not a comedy is:
\[ \boxed{\frac{2}{3}} \]
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