During a 52-week period, a company paid overtime wages for 19 weeks and hired te

Question

During a 52-week period, a company paid overtime wages for 19 weeks and hired temporary help for 8 weeks. During 4 weeks, the company paid overtime and hired temporary help complete parts (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 hep wages? P (overtime wages or temporary help wages) = (Round to the nearest thousandth as needed.)

Explanation / Answer

Solution:

a) No
Let A denote the event that the selected week contain over time wages and B denote the event the selected week contain temporary help wages.

Given that P(A) = 19/52
       P(B) = 8/52
       P(AB) = 4/52
For mutually exclusive events P(AB) =0
Since P(AB) 0, we can conclude that “Selecting the week that contained overtime wages", and "selecting a week that contained temporary help wages" mutually exclusive are not mutually exclusive.

b) A2 be the event that the payroll for the next week contained overtime wage or temporary help wage. Let A1 the payroll for the current week contained overtime wage or temporary help wage. Clearly A1 and A2 are independent. For independent events , P(A2|A1) =P(A2)

Thus P(A2) = P(AB)
       = P(A)+P(B)- P(AB)
       = 19/52+8/52 -4/52=
       = 23/52

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