Question

a machining company employs two operators---Mark and Daniel to man its machine (lathes). In a given work day, Mark has probability of 0.1 of being absent, while daniel, a new employee has 0.12. If Mark is absent, Daniel has a probability of 0.3 of being absent too.

A. What is the probability that Mark's first absent during the month occurs on or before the month's 5th work day?

B. What is the probability that daniel's second absence will happen on or after the 13th workday of his employment?

C. Find the probability that both are simultaneously absent in exactly one day in a 20 work-day month?

Answer 1

a) probability that Mark's first absent during the month occurs on or before the month's 5th work day =1-P(not absent in first 5 days)=1-(1-0.1)⁵ =0.40951

b)

probability that daniel's second absence will happen on or after the 13th workday of his employment =P(at most 1 absence in first 12 days) =P(X=0)+P(X=1)

=(12C0)*(0.12)⁰(0.88)¹²+(12C1)*(0.12)¹(0.88)¹¹=0.5686

c)

probability that they both are simultaneously absent =0.1*0.3 =0.03

probability that both are simultaneously absent in exactly one day in a 20 work-day month

=(20C1)*(0.03)¹(0.97)¹⁹ =0.3364