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An average of 8 Illinois residents die per day due to opioid overdose. Let us consider that the number of opioid overdose deaths per day in Illinois follows a Poisson distribution with an average of 8.

What is the probability of having at least one opioid overdose death on a given day?

The number of admissions of COVID patients requiring intensive care in a given hospital follows a Poisson distribution and has averaged 2 per day. The hospital has 3 beds available today in the COVID intensive care unit (ICU).

What is the probability that the hospital will refuse at least one COVID patient requiring intensive care today because the ICU will end up full?