Casey is going to wear a gray sportcoat and is trying to decide what tie he should wear to work. In his closet, he has 38 ties, 28 of which he feels go well with the sportcoat. If Casey selects one tie at random, determine the probablity and the odds of the tie going well or not going woll with the sportcoat.
The probability the tie goes well with the jacket is $\square$. (Simplify your answer. Type an integer or a fraction.)

Step 1 ：Casey has a total of 38 ties in his closet, 28 of which he feels go well with his gray sportcoat.

Step 2 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.

Step 3 ：In this case, the favorable outcome is the tie going well with the sportcoat, and the total number of outcomes is the total number of ties.

Step 4 ：So, we need to divide the number of ties that go well with the sportcoat by the total number of ties, which is \( \frac{28}{38} \).

Step 5 ：This gives us a decimal probability of approximately 0.737.

Step 6 ：However, the question asks for the answer in simplified fraction form.

Step 7 ：To convert the decimal to a fraction, we simplify \( \frac{28}{38} \) to \( \frac{14}{19} \).

Step 8 ：Final Answer: The probability the tie goes well with the jacket is \( \boxed{\frac{14}{19}} \).