Question: The electronics fabrication plant in Exercise has a third machine, machine C, which is used in periods of peak demand and is also capable of producing a batch of 50 electrical components per hour. Let E1, E2 be as in Exercise 6, and E3 be the corresponding event for machine C. The probabilities of E3, E1 ∩ E3, E2 ∩ E3, and E1 ∩ E2 ∩ E3 are 0.9, 0.87, 0.85, and 0.82, respectively. Find the probability that at least one of the machines will produce a batch with no defectives.
Exercise: Each of the machines A and B in an electronics fabrication plant produces a single batch of 50 electrical components per hour. Let E1 denote the event that, in any given hour, machine A produces a batch with no defective components, and E2 denote the corresponding event for machine B. The probabilities of E1, E2, and E1 ∩ E2 are 0.95, 0.92, and 0.88, respectively. Express each of the following events as set operations on E1 and E2, and find their probabilities.
(a) In any given hour, only machine A produces a batch with no defects.
(b) In any given hour, only machine B produces a batch with no defects.
(c) In any given hour, exactly one machine produces a batch with no defects.
(d) In any given hour, at least one machine produces a batch with no defects.