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25 March, 02:38

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?

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  1. 25 March, 02:42
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    P (A ∪ B) = 0.23

    Step-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) = 0.1

    P (B) = 0.15

    P (A ∩ B) = 0.02

    The probability that a injured worker is admitted to the hospital and is back the next day represents the intersection of both events

    P (A ∪ B) = 0.1 + 0.15 - 0.02 = 0.23
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