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 companys 205 employees, a manager asked which piece of clothing the employee prefers. the preferences, based on gender, are summarized in the table below.

	shirt	jacket
female	48	30

suppose 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.
(a) what is the probability that the employee is male and prefers a shirt?
(b) what is the probability that the employee is male or prefers a shirt?

Explanation:

Step1: Calculate total number of employees

The total number of employees is $59 + 68+48 + 30=205$.

Step2: Calculate probability for part (a)

The number of male employees who prefer a shirt is 59. The probability $P(\text{male and shirt})$ is the number of male - shirt - preferring employees divided by the total number of employees. So $P(\text{male and shirt})=\frac{59}{205}\approx0.29$.

Step3: Calculate number of male or shirt - preferring employees

The number of male employees is $59 + 68 = 127$, the number of employees who prefer a shirt is $59+48 = 107$, and the number of male employees who prefer a shirt is 59. Using the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, we have $P(\text{male or shirt})=\frac{127 + 107-59}{205}=\frac{175}{205}\approx0.85$.

Answer:

(a) $0.29$
(b) $0.85$