During a 52-week period, a company paid overtime wages for 17 weeks and hired te

Question

During a 52-week period, a company paid overtime wages for 17 weeks and hired temporary help for 7 weeks. During 4 weeks, the company paid overtime and hired temporary help. complete parts (a) and (b) below. (a) Are the events "selecting a week that contained overtime wages" and "selecting a week that contained temporary help wages" mutually exclusive? No Yes (b) If an auditor randomly examined the payroll records for only one week, what is the probability that the payroll for that week contained overtime wages or temporary help wages? P(overtime wages or temporary help wages) =

Explanation / Answer

a) The two events are not mutually exclusive. This is because of the simple reason that there are some weeks when both of the events happened at the same time that is there are 4 weeks, when the company paid for overtime and hired temporary help.

b) Now here we are given that:

total weeks = 52

Number of weeks when the company paid overtime wages = 17

Number of weeks when the company hired temporary help = 7

Number of weeks when the company paid overtime wages and hired temporary help = 4

Therefore by addition law number of weeks when company paid overtime wages or hired temporary help would be

= Number of weeks when the company paid overtime wages + Number of weeks when the company hired temporary help - Number of weeks when the company paid overtime wages and hired temporary help

= 17 + 7 - 4 = 20 weeks

Therefore the required probability would be:

= Number of weeks when company paid overtime wages or hired temporary help/ Total number of weeks

= 20/52

= 0.385

Therefore 0.385 is the required probability here.

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