Question
2. At a certain company, 40% of the employees are certified to operate machine A, 50% are certified to operate machine B, 40% are certified to operate machine , 15% are certified to operate machines A and B. i0% are certified to operate machine 5% are certified to operate all three machines, and 15% are certified to operate machine C but neither machine A nor machine B. Let A denote the event that a randomly chosen employee is certified to operate machine A, let B denote the event that a randomly chosen employee is certifed to operate machine B, and let C denote the event that a randomly chosen employee is certified to operate machine C. For each of the following, include an expression for the event in terms of set operations on A, B and C, and justify your answer s A and C, (a) Find the probability that a randomly chosen employee is certified to operate at exactly one of the three machines. (b) Find the probability that a randomly chosen employee is c A and machine C but not machines B (c) Find the probability that a randomly chosen employee is certified to operate two of the ertified to operate machine three machines but not all three. (d) Find the probability that a randomly chosen employee is certifed to operate at least one of the three machines
Explanation / Answer
P(A) = 0.4
P(B)=0.5
P(C)=0.4
P(A B) = 0.15
P(A C) = 0.1
P(A B C) = 0.05
P(C)- P(A C)- P(A B)= 0.15
P(C B)= 0.2
a) P( exactly one of the 3 machines ) = 1- P(two of the machines + 3 of the machines)
b) P(A C)- P(A B C) =0.05
c) P(A B)+ P(A C)+ P(C B)-3* P(A B C) = 0.3
d) P(atleast 1) =P(A B C) = P(A)+ P(B)+ P(C)-[ P(A B)+ P(A C)+ P(C B)]+ P(A B C) = 0.9
