A company has both male and female employees. The company has shirts and jackets with the company logo to give away to employees. For each of the company's 215 employees, a manager asked which piece of clothing the employee prefers. The preferences, based on gender, are summarized in the table below.ShirtJacketMale54 69Female79 13Suppose an employee of the company is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a)What is the probability that the employee prefers a jacket?(b)What is the probability that the employee is male or prefers a jacket?
Question
A company has both male and female employees. The company has shirts and jackets with the company logo to give away to employees. For each of the company's 215 employees, a manager asked which piece of clothing the employee prefers. The preferences, based on gender, are summarized in the table below.ShirtJacketMale54 69Female79 13Suppose an employee of the company is chosen at random.Answer each part. Do not round intermediate computations, and round your answers to the nearest hundredth.(If necessary, consult a list of formulas.)(a)What is the probability that the employee prefers a jacket?(b)What is the probability that the employee is male or prefers a jacket?
Solution
(a) To find the probability that the employee prefers a jacket, we need to calculate the ratio of the number of employees who prefer a jacket to the total number of employees.
From the table, we can see that there are 69 male employees who prefer a jacket and 13 female employees who prefer a jacket. So, the total number of employees who prefer a jacket is 69 + 13 = 82.
The total number of employees is given as 215.
Therefore, the probability that the employee prefers a jacket is 82/215 ≈ 0.3814.
(b) To find the probability that the employee is male or prefers a jacket, we need to calculate the ratio of the number of employees who are male or prefer a jacket to the total number of employees.
From the table, we can see that there are 54 male employees who prefer a shirt, 69 male employees who prefer a jacket, 79 female employees who prefer a shirt, and 13 female employees who prefer a jacket.
The total number of employees who are male or prefer a jacket is 54 + 69 + 13 = 136.
Therefore, the probability that the employee is male or prefers a jacket is 136/215 ≈ 0.6326.
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