7. An industrial plant is conducting a study to determine how quickly injured workers are back on the job following injury. Records show that 10% of all injured workers are admitted to the hospital for treatment and 15% are back on the job the next day. In addition, studies show that 2% are both admitted for hospital treatment and back on the job the next day. a. If a worker is injured, what is the probability that the worker will either be admitted to a hospital or be back on the job the next day or both?b. What is the probability that an admitted worker not to be back on job the next day?

Answer:P(A ∪ B ) = 0.23Step-by-step explanation:When 2 events are non mutually exclusive you have the following formula for one of them or both :P(A ∪ B ) = P(A) + P(B) - P(A ∩ B)for this problem using A for injured workers admitted to the hospital and B for the injured workers back on the next day. you have:P(A) = 0.1P(B) = 0.15P(A ∩ B) = 0.02The probability that a injured worker is admitted to the hospital and is back the next day represents the intersection of both eventsP(A ∪ B ) = 0.1 + 0.15 - 0.02 = 0.23