Question

3)- Records at an industrial plant show that 12% of all injured workers are admitted to a hospital for treatment, 16% are back on the job the next day, and 2% are both admitted to a hospital for treatment and back on the job the next day. If a worker is injured, what is the probability that the worker will be either admitted to a hospital for treatment, or back on the job the next day, or both?

Answer 1

The probability that an injured worker will be either admitted to a hospital for treatment, or back on the job the next day, or both is 26%.

Step-by-step explanation:

To calculate the probability that an injured worker will be either admitted to a hospital for treatment, or back on the job the next day, or both, we use the formula for the probability of the union of two events A and B, which is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

In this case, let A be the event that an injured worker is admitted to a hospital for treatment (with a probability of 12%, or 0.12) and let B be the event that an injured worker is back on the job the next day (with a probability of 16%, or 0.16). The probability of both events occurring (an injured worker being admitted to the hospital and being back on the job the next day) is 2%, or 0.02.

So the probability that an injured worker will be either admitted to a hospital for treatment, or back on the job the next day, or both is:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.12 + 0.16 - 0.02
= 0.26 or 26%