Daily probability of full COVID-bed occupancy at a health centre is 0.8. Under the binomial model, find probability of exactly five full-occupancy days in a seven-day week, to three decimals.
There are seven independent daily trials under the stated model. Exactly five successes have probability C(7, 5)×0.8⁵×0.2². Since C(7, 5)=21, this equals 0.2752512, or 0.275. The binomial coefficient counts which five days have full occupancy.
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