某家电子商务网站的长期转化率为10%。假设长期转化率不变且转化活动相互独立。 a.The website just failed to convert 9 customers in a row. What is the probability that the site will convert the next customer? 该网站此前连续转化9个客户都失败，请问该网站成功转化下一个客户的概率是多少？ b.What is the probability that for the next 10 customers, the site will convert the 1st, 3rd and 5th customers and fail to convert all others? 在接下来的10个客户中，该网站成功转化第1个、第3个和第5个客户，且其余客户均转化失败的概率是多少？ c.What is the probability that the site will convert 3 customers of the next 10 customers? 在接下来的10个客户中，该网站成功转化3个客户的概率是多少？
理解问题某家电子商务网站的长期转化率为10%。假设长期转化率不变且转化活动相互独立。 a.The website just failed to convert 9 customers in a row. What is the probability that the site will convert the next customer? 该网站此前连续转化9个客户都失败，请问该网站成功转化下一个客户的概率是多少？ b.What is the probability that for the next 10 customers, the site will convert the 1st, 3rd and 5th customers and fail to convert all others? 在接下来的10个客户中，该网站成功转化第1个、第3个和第5个客户，且其余客户均转化失败的概率是多少？ c.What is the probability that the site will convert 3 customers of the next 10 customers? 在接下来的10个客户中，该网站成功转化3个客户的概率是多少？
已完成理解「某家电子商务网站的长期转化率为10%。假设长期转化率不变且转化活动相互独立。 a.The website just failed to convert 9 customers in a row. What is the probability that the site will convert the next customer? 该网站此前连续转化9个客户都失败，请问该网站成功转化下一个客户的概率是多少？ b.What is the probability that for the next 10 customers, the site will convert the 1st, 3rd and 5th customers and fail to convert all others? 在接下来的10个客户中，该网站成功转化第1个、第3个和第5个客户，且其余客户均转化失败的概率是多少？ c.What is the probability that the site will convert 3 customers of the next 10 customers? 在接下来的10个客户中，该网站成功转化3个客户的概率是多少？」
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- 转化率是10%，即0.1。
a. 连续失败9次后转化下一个客户的概率
- 转化概率：0.1
- 连续失败概率：$0.9^9$
- 转化下一个客户的概率：$1 - 0.9^9$
b. 特定顺序转化3个客户的概率
- 转化第1、3、5个客户的概率：$0.1^3$
- 其余7个客户失败的概率：$0.9^7$
- 总概率：$0.1^3 * 0.9^7$
c. 转化3个客户的概率
- 二项分布公式：$P(X=k) = C(n, k) * p^k * (1-p)^{n-k}$
- 具体计算：$C(10, 3) * 0.1^3 * 0.9^7$
