In Bill the Boring's dryer there are 19 black shirts, 6 gray shirts, 2 black sweaters, and 4 gray sweaters. Bill is going to take one of these pieces of clothing out of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a sweater? Do not round intermediate computations, and round your answer to the nearest hundredth.

Step 1 ：In Bill the Boring's dryer there are 19 black shirts, 6 gray shirts, 2 black sweaters, and 4 gray sweaters. Bill is going to take one of these pieces of clothing out of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a sweater?

Step 2 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the favorable outcomes are the events where the piece of clothing is gray or a sweater. The total number of outcomes is the total number of pieces of clothing in the dryer.

Step 3 ：Let's denote the number of black shirts as \(black\_shirts = 19\), the number of gray shirts as \(gray\_shirts = 6\), the number of black sweaters as \(black\_sweaters = 2\), and the number of gray sweaters as \(gray\_sweaters = 4\).

Step 4 ：The total number of clothes in the dryer is \(total\_clothes = black\_shirts + gray\_shirts + black\_sweaters + gray\_sweaters = 31\).

Step 5 ：The favorable outcomes are the events where the piece of clothing is gray or a sweater, which is \(favorable\_outcomes = gray\_shirts + gray\_sweaters + black\_sweaters = 12\).

Step 6 ：The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes, which is \(probability = \frac{favorable\_outcomes}{total\_clothes} = 0.3870967741935484\).

Step 7 ：Rounding to the nearest hundredth, the final answer is \(\boxed{0.39}\).