Question

概率题～谢谢各位大师啦！！！帮个忙～～～

平均200件产品有一个不合格，则一个共500件的样品，其中，1：没有一个错误的概率。 2：四个以内错的概率. 谢谢各位大师啦！！！
An auditor's check of invoices showed that there was an average of 1 error per 200 invoices. If a sample of 500 invoices is taken what is the probability
a):none of the invoices contains an error?
b):less than foru of the invoices contain an error?
两位答案都特好～不过因为第二位有答案～所以～～不过真是谢谢啦！

Answer 1

a 0．995的500次方
b (199/200)^500+ C(500,1)(1/200)*[(199/200)^499]+C(500,2)[(1/200)^2]*[(199/200)^498]+C(500,3)[(1/200)^3]*[(199/200)^497]=75.784258%

Answer 2

(199/200)^500=0.08157

(199/200)^500+(199/200)^499*500/200+(199/200)^498*(500*499/2)/200^2+(199/200)^497*(500*499*498/3/2)/200^3=
懒得算了