Question

一道数学概率问题 英文题目哦

(a) In the national lottery, you identify 6 balls from a set of 49 balls. Then 6 balls are selected at random from the 49 balls and you get a prize if at least 3 of these match the balls you identified. (Ignoring the bonus ball for now)
---What is the probability that you get a prize of some sort?
(b) actually it is more complicated; after the 5 balls are selected at random, a sixth “bonus” ball is selected at random and you get a special kind of prize if, of the six balls you identified, 5 were in the selected group of six and the sixth is the bonus ball (as well as all the prizes for matching 3 or more of the first six balls)
---What is the probability you get a special kind of prize just described?
---Keeping this in mind, what is the probability that you get a prize of some sort?

Answer 1

Solution
(a):If this problem needn't arrange all balls in a sequence.
3_balls:1/18424
4_balls:1/211876
5_balls:1/1906884
6_balls:1/13983816
(b):
The probability that get a special kind of prize is 1/44;
Without bonus
3_balls:1/18424
4_balls:1/211876
5_balls:1/1906884

With bonus
2+1_balls:1/51744
3+1_balls:1/810656
4+1_balls:1/9322544
5+1_balls:1/83902896