Questions: In Bill the Boring's dryer there are 5 gray shirts, 10 black sweaters, and 4 gray sweaters. But, there are no black shirts. 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 black or is a shirt? Do not round intermediate computations, and round your answer to the nearest hundredth.

In Bill the Boring's dryer there are 5 gray shirts, 10 black sweaters, and 4 gray sweaters. But, there are no black shirts. 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 black or is a shirt? Do not round intermediate computations, and round your answer to the nearest hundredth.
Transcript text: In Bill the Boring's dryer there are 5 gray shirts, 10 black sweaters, and 4 gray sweaters. But, there are no black shirts. 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 black or is a shirt? Do not round intermediate computations, and round your answer to the nearest hundredth. (If necessary, consult a list of formulas.) $\square$
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Solution

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Solution Steps

Step 1: Calculate the Total Number of Items

Total number of items = n_bs + n_gs + n_bw + n_gw = 19

Step 2: Identify the Items of Interest

Items of color black = 10, Items of type shirt = 5, Items both black and shirt = 0

Step 3: Calculate the Probability

P(interest) = (n_color + n_type - n_both) / Total = 0.79

Final Answer:

The probability of selecting an item that is either black or a shirt is 0.79.

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