In Bill the Boring's dryer there are 15 black shirts, 7 gray shirts, 9 black sweaters, and 6 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 plece of clothing Bill takes out is black or is a shirt? Do not round intermediate computations, and round your answer to the nearest hundredth.

To find the probability that the piece of clothing Bill takes out is black or is a shirt, we first need to determine the total number of clothing items and how many of them meet the criteria. Bill has the following clothing items: - 15 black shirts - 7 gray shirts - 9 black sweaters - 6 gray sweaters **Total number of items:** 15 (black shirts) + 7 (gray shirts) + 9 (black sweaters) + 6 (gray sweaters) = 37 items **Number of black items:** - Black shirts: 15 - Black sweaters: 9 Total black items = 15 + 9 = 24 **Number of shirts:** - Black shirts: 15 - Gray shirts: 7 Total shirts = 15 + 7 = 22 **Number of items that are either black or shirts:** To avoid double counting, we can use the principle of inclusion-exclusion. Total (black or shirt) = Number of black items + Number of shirts - Number of black shirts = 24 + 22 - 15 = 31 **Probability:** Now, the probability that the piece of clothing Bill takes out is black or is a shirt is the number of favorable outcomes divided by the total outcomes: Probability = Number of favorable outcomes / Total items = 31 / 37 ≈ 0.8378 Rounding to the nearest hundredth, the probability is approximately **0.84**.