Answer to Question #123390 in Statistics and Probability for LaDean

Question

Question 1: A company has made available to its employees (without charge) extensive health club facilities that may be used before work, during the lunch hour, after work, and on weekends. Records for the last year indicate that of 250 employees, 110 used the facilities at some time. Of 170 males employed by the company, 65 used the facilities. What is the probability that an employee chosen at random.




d. Is a female or has used the health club facilities?
e. Given that the selected employee is female, what is the probability that she has used the health club facilities?
f. Given that the selected employee is male, what is the probability that he has not used the health club facilities?

Answer 1

$$\def\arraystretch{1.5} \begin{array}{c:c:c} & Use & Don't \ use & Total\\ \hline Female & 45 & 35 & 80 \\ \hdashline Male & 65 & 105 & 170 \\ \hdashline Total & 110 & 140 &250 \end{array}$$

d.

$$P(Female\ or\ Use)=$$

$$=P(Female)+P(Use)-P(Female\ and\ Use)=$$

$$={80 \over 250}+{110 \over 250}-{45 \over 250}={145 \over 250}=$$

$$={145 \over 250}={29 \over 50}=0.58$$

e.

$$P(Use|Female)={45\over 80}={9 \over 16}=0.5625$$

f.

$$P(Don't\ use|Male)={105 \over 170}={21 \over 34}\approx0.617647$$