题目
During an annual beach-clean, the people doing the clean are asked to conduct a litter survey. At a particular beach-clean, litter was found at a rate of 4 items per square metre.
(a) Find the probability that, in a randomly selected area of 2 square metres on this beach, exactly 5 items of litter were found.
Of the litter found on the beach, 30% of the items were face masks.
(b) Find the probability that, in a randomly selected area of 5 square metres on this beach, more than 4 face masks were found.
(c) Using a suitable approximation, find the probability that, in a randomly selected area of 20 square metres on this beach, less than 60 items of litter were found that were not face masks.
(Total for Question 1 is 8 marks)
题目中文翻译
在一次年度海滩清洁活动中，清洁人员被要求进行垃圾调查。在一次特定的海滩清洁中，垃圾的发现速率为每平方米 4 件。
(a) 求在此海滩上随机选择的 2 平方米区域内恰好发现 5 件垃圾的概率。
在海滩上发现的垃圾中，30% 为口罩。
(b) 求在此海滩上随机选择的 5 平方米区域内发现超过 4 个口罩的概率。
(c) 使用适当的近似方法，求在此海滩上随机选择的 20 平方米区域内发现少于 60 件非口罩垃圾的概率。
（第 1 题共 8 分）