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 The Random Problem (Posted on 2004-02-09)
Suppose there are 20 problems on the site the Sunday evening a user looks at the site the first time. She doesn't read the newest problem of the day, but instead ONLY reads problems that come up on the "Random Problem" page. She reads 5 random problems each day, always in the evening. The only problem is she can see the same problem more than once.

The other problem is problems continue to come in from the infinite queue. Two per week day and one per weekend.

What is the probability she will have read all the problems after her next Sunday evening check? What is the probability she will have read all the problems after the Sunday evening after that?

Note: The problems displayed when you click on "Random Problem" are independent of each other. There isn't anything to make sure that you are getting five different problems if you click on random problem five times.

 See The Solution Submitted by Gamer Rating: 4.1429 (7 votes)

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 Question for Gamer | Comment 3 of 8 |
Gamer, are the following assumptions correct? If they are, I will have to wait to solve this one until my programming skills with Visual Basic are properly developed. I'm still going through the course materials.

Assumptions: 2 new problems come in, each at any random time of the day or night, each weekday, and 1 new problem comes in at any random time of the day or night, each weekend (Saturday or Sunday). The Random button is truly random. The possibilities for the number of puzzles on the website when she clicks on Random button five times each evening then are:

Sunday evening:

20-20-20-20-20
20-20-20-20-21
20-20-20-20-22
20-20-20-21-21
20-20-20-21-22
20-20-20-22-22
20-20-21-21-21
20-20-21-21-22
20-20-21-22-22
20-21-21-21-21
20-21-21-21-22
20-21-21-22-22
20-21-22-22-22
20-22-22-22-22

Monday evening:

22-22-22-22-22
22-22-22-22-23
22-22-22-22-24
22-22-22-23-23
22-22-22-23-24
22-22-22-24-24
22-22-23-23-23
22-22-23-23-24
22-22-23-24-24
22-23-23-23-23
22-23-23-23-24
22-23-23-24-24
22-23-24-24-24
22-24-24-24-24
23-23-23-23-23
23-23-23-23-24
23-23-23-24-24
23-23-24-24-24
23-24-24-24-24
24-24-24-24-24

Tuesday evening:

24-24-24-24-24
24-24-24-24-25
24-24-24-24-26
24-24-24-25-25
24-24-24-25-26
24-24-24-26-26
24-24-25-25-25
24-24-25-25-26
24-24-25-26-26
24-25-25-25-25
24-25-25-25-26
24-25-25-26-26
24-25-26-26-26
24-26-26-26-26
25-25-25-25-25
25-25-25-25-26
25-25-25-26-26
25-25-26-26-26
25-26-26-26-26
26-26-26-26-26

Etc...............................
 Posted by Penny on 2004-02-09 18:03:15

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